Given:
2+4+6+8+10+.....+50
[tex]2+4+6+10+\cdots+50=2(1+2+3+\cdots+25)[/tex]Let the sum of the first n natural numbers be
[tex]S_n=\frac{n(n+1)}{2}[/tex]Therefore the sum of first 25 positive even numbers is
[tex]2S_n=\frac{2n(n+1)}{2}[/tex][tex]2S_n=n(n+1)[/tex]Therefore,The sum is the product of the number of terms and the number of terms plus one.
Option B is the correct answer.
Determine algebraically if f(x)=|x+2|is a functioneven, odd, or neither.
The absolute value function is given below as
[tex]f(x)=|x+2|[/tex]Concept: We will have to explain what is meant by an odd function, even function, or neither
Even function: A function is said to be even if it has the equality below
[tex]f(x)=f(-x)[/tex]is true for all x from the domain of definition.
An even function will provide an identical image for opposite values.
Odd function:A function is odd if it has the equality below
[tex]f(x)=-f(-x)[/tex]is true for all x from the domain of definition.
An odd function will provide an opposite image for opposite values.
Neither: A function is neither odd nor even if neither of the above two qualities is true, that is to say:
[tex]\begin{gathered} f(x)\ne f(-x) \\ f(x)\ne-f(-x) \end{gathered}[/tex]Given that
[tex]\begin{gathered} f(x)=|x+2| \\ f(-x)=|-x+2| \\ f(x)\ne f(-x) \end{gathered}[/tex]Also,
[tex]\begin{gathered} f(x)=|x+2| \\ -f(-x)=-|-x+2| \\ f(x)\ne-f(-x) \end{gathered}[/tex]Therefore,
We can conclude that f(x) = |x+2| is NEITHER an even nor a odd function
Eight minus six and two-fifths
Answer:
1 and three-fifth or 1.6
write an equation of the line described
passes through (8,8)
parallel to the line y = -7/4x - 4
Answer:
y = -7/4x + 22
Step-by-step explanation:
linear equation: y = mx +c, where m is the slope
when a line is parallel to another line, it means they have same slope
so the line slope, m = -7/4
now you need to find c to complete the equation
you have x,y information
replace that into linear equation together with slope value
8 = (-7/4)8 + c
8 = -14 + c
8+14 = c
c = 22
substitute m,c into the equation, you get
y = -7/4x + 22
Anta's sister was born when he was exactly three years old. If the product of their ages is 1404, how old are they now?
Answer need to be.(36 and 39)
I need step by step
Thank you
Answer:
Below
Step-by-step explanation:
Anta = x sister = x+3 <======given in the question
x * x+3 = 1404
x^2 + 3x - 1404 = 0 Use quadratic formula with a = 1 b= 3 c = -1404
to find x = 36 and sister = 36 + 3 = 39 y/o
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The point of maxima of any function can be known by equating its derivative to zero. The rocket will take 1.5 sec to reach the maximum height and the maximum height is 27 feet.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric aspect is the slope of the function at a given point.
Given that,
Initial height of the launching pad is 4 feet,
Initial velocity of rocket is 48 feet/sec,
Height of the rocket as a function of time, h(t) = -16t² + 48t + 3
In order to find the time for maximum height equate h'(t) = 0 as follows,
-32t + 48 = 0
⇒ t = 48 / 32
⇒ t = 3 / 2
⇒ t = 1.5
To find the maximum height find h(t) for t = 1.5 as follows,
h(1.5) = -16 × 1.5² + 48 × 1.5 + 3
= -36 + 60 + 3
= -36 + 63
= 27
Hence, the time taken by the rocket to reach the maximum height is 1.5 sec and the maximum height reached is 27 feet.
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How do u Arranging the order of polynomials
Answer: You must put the highest exponent of the variable first, and then proceed in descending order.
Step-by-step explanation:
This is done to keep track of the powers much easier and also just looks nicer. ^^
I need help creating an equation to match the table
Let x be "the number of hours worked"
And y be "Amount of money earned"
If both variables vary proportionality, you can say that the constat of proportionality is
[tex]k=\frac{y}{x}[/tex]Choosing one pair of values of the table:
For example x=2 and y=125
Assuming the flat fee the painter changes is 25 (I choose it to be 25 because the variation turns proportional if you subtract 25 fromm all values of y)
Then subtract it from the value of y
125-25=100
And use it to calculate the the constant k
[tex]k=\frac{100}{2}=50[/tex]So the painter earns $50 per hour worked
The function is then y=25+50x
The correct option is the first one.
Which value of x makes this inequality true? 12x-6 < 30 A. X< 36 B. x > 2 C. x 24
Hi I need help on finding the answer to this question attached in picture
We know that the linear model:
[tex]c=2.20+2m[/tex]To determine the cost for a given mileage we just need to plug the later in the equation; in this case we know that m=16, then we have:
[tex]\begin{gathered} c=2.20+2(16) \\ c=2.20+32 \\ c=34.20 \end{gathered}[/tex]Therefore, it cost $34.20 to travel sixteen miles.
The table below gives select values for the differentiable function f and g, and f' , the derivative of f, at select values of x. If...
Answer: for this problem. What we're going to do essentially, this is an exercise of using the formula for finding the derivative of the inverse of a function. So we have the derivative of the inverse of F would be equal to one over the derivative of F. So F prime evaluated at f inverse of X. So in this case we have X equals three. So F inverse of three, prime will be equal to one over F prime evaluated at f inverse of three. Now, looking at the table of values that you have, well, F inverse of three is going to be the X value such that X equals, or the the X values such that F equals three. So we can see that F equals three when X equals negative one. So we have one over F prime evaluated at negative one and F prime of negative one, we can see it is equal to one. So we'd have won over one or just one is the final answer.
Step-by-step explanation:
The price of fuel changed from $3.50 per gallon to $3.20 per gallon.
The percentage change though = 25%.
What is Percentage?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.
Bob's price dropped by $0.30, or BLANK, between April 1 and May 1.
Considering that the initial price was $3.20, the percentage change was 0.3/3.2, or 9.37%.
Bob's cost grew by $0.30 between May 1 and June 1 (or BLANK).
Price change was -0.3/3.5 = -8.57% since the initial price was $3.50.
Consider that the prices at the gas station across the street are consistently 20% more than those at Bob's. When gas costs $3.50 instead of $3.20, the price difference between Bob's and the prices across the street is BLANK in absolute terms.
Since 20% of $3.50 is greater than 20% of $3.20, the absolute difference will be greater when gas costs $3.50.
Let's say the Federal Reserve increases the federal funds rate objective from 2% to 2.5%. The Fed increased its target by almost BLANK percentage points as a result of this change.
It is 1% for each percentage point. Half a percentage point is the difference between 2% and 2.5%. However, the percentage change was 25% (0.5/2).
Hence, The percentage change is 25%
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A bottle rocket is launched straight up. Its height in feet (y) above theground x seconds after launch is modeled by the quadratic function: y =-16x2 + 132x + 6.How many seconds did it take the rocket to reach its maximum height?
Answer:
(C)4.125 seconds
Explanation:
The quadratic function modeling the rocket's movement is:
[tex]y=-16x^2+132x+6[/tex]To determine the number of seconds it takes the rocket to reach its maximum height, we are being asked to find the equation of the line of symmetry.
For a quadratic function of the form y=ax²+bx+c, the equation of the line of symmetry is:
[tex]x=-\frac{b}{2a}[/tex]In the given equation:
a = -16, b = 132
Therefore:
[tex]\begin{gathered} x=-\frac{132}{-2\times16} \\ x=4.125 \end{gathered}[/tex]It takes the rocket 4.125 seconds to reach its maximum height.
can yall help me with this
The resultant answer after solving the given expression is (C) 2/3.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.So, solve for ⁴√16/81:
Apply radical rule as follows:
⁴√16/81⁴√16/⁴√81We know, ⁴√16 = 2.
Then,
2/⁴√81 ⁴√81 = 3Then,
2/3Therefore, the resultant answer after solving the given expression is (C) 2/3.
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What is the value of 13(a • b + a2) + 4 if a = 5 and b = −3?
308
134
−74
−126
please helpppppp
i need you if you get correct ill give brainlyest
need now
The value of the expression 13(a • b + a²) + 4 if a = 5 and b = −3 is B 134.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
The expression is illustrated thus:
13(a • b + a²) + 4
= 13(5 • (-3) + 5²) + 4
= 13(-15 + 25) + 4
= (13 × 10) + 4
= 130 + 4
= 134
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I have taken a picture of the question I am needing help with. Thank you.
Answer:
Width: 20 in
Length: 25 in
Explanation:
We can represent the situation with the following figure
Where x is the width of the rectangular piece of metal, (x + 5) is the length of the rectangular because it is 5 in longer than its wide, and the corners have squares of side 1 in.
Therefore, the volume of the box will be equal to
Volume = Length · Width · Height
Volume = (x + 5 - 1 - 1) · (x - 1 - 1) · (1)
Volume = (x + 3)(x - 2)(1)
Volume = (x + 3)(x - 2)
Because the length of the box will be the length of the rectangle less the length of the squares and the width of the box will be the length of the rectangle less the width of the squares.
The volume is 414 in³, so we need to solve the following equation:
414 = (x + 3)(x - 2)
414 = x² + 3x - 2x + 3(-2)
414 = x² + x - 6
414 - 414 = x² + x - 6 - 414
0 = x² + x - 420
Factorizing x² + x - 420, we get:
(x + 21)(x - 20) = 0
Then
x + 21 = 0
x + 21 - 21 = 0 - 21
x = -21
or
x - 20 = 0
x - 20 + 20 = 0 + 20
x = 20
Since x = -21 doesn't have sense, the width is x = 20 and the length is:
x + 5 = 20 + 5 = 25 in.
So, the original width is 20 in and the original length is 25 in
18. Find m∠VSW if ∠WSR and ∠VSW are complementary and m∠WSR is four times m∠VSW. A 72 C 22.5 B 36 D 18
We will have the following:
First, we have that:
[tex]m<\text{VSW}+m<\text{WSR}=90[/tex]And we have that:
m[tex]m<\text{VSW}+4m<\text{VSW}=90\Rightarrow5m<\text{VSW}=90[/tex][tex]\Rightarrow m<\text{VSW}=18[/tex]So, the measurement of angle VSW is 18°.
The length of a rectangle is 3 meters greater than 2 times the width. The perimeter of rectangle is 30 meters. What is the length of the rectangle?
The length of a rectangle of the rectangle is 11m.
What is a rectangle?A rectangle is a polygon with four sides and four angles. Each angle is 90° and it has two lines of symmetry.
let the length of the rectangle be L and the width be w, so that
L = 3 + 2w
Also perimeter = 2 ( L + w)
2( L + W) = 30
substitute L = 3 + 2W into the above equation
2( 3 + 2W + W) = 30
2(3 +3W) = 30
multiply the bracket by 2
6 + 6W = 30
6W = 24
W = 24/6
W = 4m
but L = 3 + 2W, when W = 4m
L = 3 + (2 x 4)
L = 3 + 8
L = 11m
In conclusion the length of the rectangle is 11m
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ASAP PLEASE
Show how we can use compensation to find the value of 8.2 x 19
Write it Step by step.
Value of the given expression 8.2 x 19 using compensation method is equal to 155.8.
As given in the question,
Given expression is equal to :
8.2 x 19
Apply compensation method to make the calculation easily and get the value of the given expression we have,
8.2 x 19
Rewrite 19 as ( 20 -1 ) we get,
= 8.2 × ( 20 - 1 )
Apply distributive law multiplication over subtraction we get,
= ( 8.2 × 20 ) - ( 8.2 × 1 )
= 164.0 - 8.2
= 155.8
Therefore, value of the given expression 8.2 x 19 using compensation method is equal to 155.8.
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Martin is a manager at a restaurant. He receives a straight commission of 8% on food sales for the month. What were his March earnings if the restaurant sold $31,902 in food?
Martin's commission earning is $2552.16
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given that, Martin receives a straight commission of 8% on food sales for the month,
31,902*8/100 = 2552.16
Hence, Martin's commission earning is $2552.16
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Lindsey bought a picnic basket originally priced at $40 but on sale for 50% off. After 10% sales tax, what was the total cost?
$
The total cost price of the basket is $22.
What is Discount ?
The discount is determined by dividing the purchase price by the item's par value. The discount is a type of cost price reduction or deduction for a product. It is primarily employed in consumer interactions when discounts on various goods are offered to customers. A percentage represents the discount rate.
Here ,
Original cost price of the basket = $40
After 50% offer the cost price of the bag is,
=> 40- 50% of 40
=> 40 - 20
=> $20.
Now the sales tax is 10% then,
=> 20+ 10% of 20
=> 20+ 2
=>$22
Therefore the total cost is $22 after discount.
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Write a quadratic function that fits the points (0, 6), (2, 4), and (3, 6).
The quadratic equation y = x² - 3 · x + 6 fits the points (0, 6), (2, 4) and (3, 6).
How to find a quadratic equation that fits a set of three points
Herein we find a set of three points that fits in a quadratic equation, that is, a polynomial of the form y = a · x² + b · x + c, where a, b, c are real coefficients. It is possible to find a quadratic equation as the number of points is equal to the numbers of real coefficients.
First, obtain the system of linear equations by substituting the values of x and y on each case:
(x, y) = (0, 6)
a · 0² + b · 0 + c = 6
c = 6
(x, y) = (2, 4)
a · 2² + b · 2 + c = 4
4 · a + 2 · b + c = 4
(x, y) = (3, 6)
a · 3² + b · 3 + c = 6
9 · a + 3 · b + c = 6
Second, solve the system of linear equations by numerical methods:
(a, b, c) = (1, - 3, 6)
Third, write the resulting quadratic equation:
y = x² - 3 · x + 6
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If the charge for shipping and handling is 8%, what is the total charge for an online order of $45?
We need to calculate the 8% of $45
[tex]45\cdot\frac{8}{100}=3.60[/tex]The total charge will be
[tex]45+3.60=48.60[/tex]ANSWER
The total charge is $48.60
Rashad chose C as the correct answer. How did he get that answer?
Answer:
He multiplies the denominator by 7.
Step-by-step explanation:
There is a raffle with 200 tickets. One ticket will win a $240 prize, three tickets will win a $90 prize, eight tickets will win a $50 prize, and the other tickets will win nothing. If you have a ticket, what is th expected payoff?
Teshawn, this is the solution:
As we had this same question before, the expected payoff is:
1/200 * 240 + 3/200 * 90 + 8/200 * 50 + 188/200 * 0
1.2 + 1.35 + 2 + 0
Therefore, the expected payoff for a raffle ticket is $ 4.55
Henry bought a car for $14, 000. After two years, the value of the car was $8, 400 What was the percent decrease in the value of the car after two years? Enter the correct number in the box.
Answer:
I think it would be 60%
Step-by-step explanation:
Write an equation of the line that passes through the point (-2,6) and is parallel to the line that passes through the points (0,-4) and (3,2)
We have the points:
p(0,-4) & q(3,2)
then, our directional vector will be:
pq(3,6)
now we have the equation of the line that we need to be parallel with:
(x,y)=(0,-4)+t(3,6)
We get (3,6) as follows:
we determine the directonal vector using the two point given:
p(0,-4) & q(3,2)
pq(3-0,2+4) =>pq=(3,6)
Now, the point of the line that is parallel to the one we got is: (-2,6):
Since a condition for being parallel is that the directional vector from one line is a product of the other, then:
(x,y) = (-2,6) + t(6,12)
As can be seen, the directional vector is parallel to the one found before (one is multiple of the other)
As for before, the equation of the line that passes by the point (-2,6) and is parallel to the line (x,y) = (0,-4) + t(3,6) is:
[tex](x,\text{ y) = (-2,6) + t(6,12)}[/tex]y=-2x+10 in standard form
Answer:Y+2x=10
Step-by-step explanation:
Answer:
2x+y=10
Step-by-step explanation:
The standard form is x+y=#
y=-2x+10
flip it around:
10-2x=y
add 2x
10=2x+y
2x+y=10
what is (2x−6)+4(x−3)
Answer:
Step-by-step explanation:
6*(x-3) yeah that is it.
Answer:
[tex]6x-18[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex]2x-6+4x-12[/tex]
Step 2: Add like terms
[tex]2x+4x[/tex]
[tex]-6-12[/tex]
Step 3: Consolidate
[tex]6x-18[/tex]
15. An object that weighs exactly 1pound is placed on a digital scalethat measures weight in ounces. Ifthe scale is precise but notaccurate, what weight might beshown on the scale?
The rate of conversion between pounds and ounces is shown as;
16 ounces = 1 pound
Then you have a digital scale that measures weight in ounces. If you put an object that weighs "exactly 1 pound" on the digital scale, its supposed to display 16 ounces.
However the scale has been described as "not accurate," which implies that the calibration (fine tuning) has been altered either accidentally or on purpose. This also implies that the result would not be 100 percent correct, but it might be a little over or below 16 ounces. Hence the scale might display what in mathematics is termed as "plus or minus" and is denoted by the sign ±
The scale therefore might display 15 ounces or 17 ounces (that is ± 16)
±
8. Write an equation of the line perpendicular to y = x + 4 that contains (3,-3). Please write the
equation in point-slope form.
Answer:
y + 3 = - (x - 3)
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x + 4 ← is in slope- intercept form
with slope m = 1
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{1}[/tex] = - 1
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - 1 and (a, b ) = (3, - 3 ) , then
y - (- 3) = - 1 (x - 3) , that is
y + 3 = - (x - 3)