36 is 17th term of sequence a₁₈ = 32, d=-4
Given the 18th term and the common difference, we subtract the common difference from the 18th term to determine the 17th term:
a₁₇ = a₁₈ - d
= 32 - (-4)
= 36
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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You buy3.9 pounds of trail mix. The mix costs $2.88 per pound. What is the total price for the trail mix?
Step-by-step explanation:
$2.88 per pound
so, then how much for e.g. 2 pounds ?
right : the price for 1 pound plus 1 pound = 2×$2.88 = $5.76
and so on.
therefore, 3.9 pound cost :
3.9 × $2.88 = $11.232 ≈ $11.23
Answer:
11.232
Step-by-step explanation:
3.9×2.88=11.232
HELP!!
Whats 2 to the power of 3 x 2 to the power of 5
Answer: 256
how do i get to it??
Answer:
(2x2x2)*(2x2x2x2x2) so 8x32 = 256
Step-by-step explanation:
Answer: Simplify {2}^{3}2
3
to 88.
8x\times {2}^{5}
8x×2
5
2 Simplify {2}^{5}2
5
to 3232.
8x\times 32
8x×32
3 Simplify.
256x
Step-by-step explanation: hope this helps!!!!
Solve for x (5x+3)=(7x-7)
answer:
5
explanation:
(5*5) + 3=28
(7*5) - 7= 28
Write an equation for each line. m=-5 and the y -intercept is (0,-7) .
The equation of the line for given values is y = -5x - 7.
Given a point and a slope, how do you build an equation for a line?When you know the slope of the line to be investigated and the provided point is also the y intercept, you may utilize the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
The standard equation of straight line is y = mx + c.
Given m = -5 and y - intercept is -7
So, the equation of the line becomes y = -5x - 7
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Divide. State any restrictions on the variable. 3x-6/12 x-24 ÷ x²5 x+6 / 3 x² - 12
The division of given rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex] is [tex]\frac{3(x-2)}{4(x+3)}[/tex] provided x ≠ -3
In this question,
we have been given a complex rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex]
We need to find the division of given rational expression.
We rewrite given rational expression as,
[tex]\frac{\frac{3x-6}{12x-24}}{\frac{x^2+5x+6}{3x^{2} -12}}\\\\\\= \frac{3x-6}{12x-24}\times \frac{3x^2-12}{x^2+5x+6}[/tex]
First we simplify the quadratic expression x² + 5x + 6
x² + 5x + 6
= x² + 3x + 2x + 6
= x(x + 3) + 2(x + 3)
= (x + 3)(x + 2)
And the simplified form of quadratic expression 3x² - 12 would be,
3x² - 12
= 3(x² - 4)
= 3(x² - 2²)
= 3(x + 2)(x - 2)
So, the given rational expression would be,
[tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12} \\\\\\ = \frac{3x-6}{12x-24}\times \frac{3x^2-12}{x^2+5x+6}\\\\\\=\frac{3(x-2)}{12(x-2)}\times \frac{3(x+2)(x-2)}{(x+3)(x+2)}[/tex]
[tex]\\\\=\frac{3}{12}\times \frac{3(x-2)}{(x+3)}\\\\\\=\frac{3(x-2)}{4(x+3)}~~~~~~~~~~~~~(provided~~x\neq -3)[/tex]
Therefore, the division of given rational expression [tex]\frac{3x-6}{12x-24}\div \frac{x^2+5x+6}{3x^{2} -12}[/tex] is [tex]\frac{3(x-2)}{4(x+3)}[/tex] provided x ≠ -3
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3) What is the perimeter of the figure
below?
Please show how you solved it.
Answer:
Multiply 2 by 9, and then 2 by 11, and add it up all together. 18+22=40
Step-by-step explanation:
help, please :) I APPRECIATE IT
a video posted on the internet is becoming very popular, and the total number of views is increasing by 30% every hour. if the video currently has 11,882 views, how many views will it have in 3 hours
Answer:26105 rounded
Step-by-step explanation: if not rounded 26104.754
Tom delivers papers on a rural route from his car. If he throws a paper from a height of 4 feet, and it lands 15 feet from the car, at what angle of depression did he throw the paper to the nearest degree?
The angle of depression, at which Tom threw the paper is 14.93°
In this question,
Tom throws a paper from a height of 4 feet, and it lands 15 feet from the car.
We need to find the angle of depression, at which he threw the paper.
Consider the following diagram.
Let the θ be the angle of depression, at which he threw the paper.
Consider the tangent of angle θ.
⇒ tan(θ) = 4/15
⇒ θ = [tex]tan^{-1}(\frac{4}{15} )[/tex]
⇒ θ = 14.93°
Therefore, the angle of depression, at which Tom threw the paper is 14.93°
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write the equation of the line that is parallel to y=1/3x-3 and passes through the point (6,2)
PLEASE HELP
[tex]\textsf{Hi Brainy User, I'm Here to Help you!}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\textsf{Parallel lines have the same slope, thus:}[/tex]
[tex].\qquad\bullet\sf{Slope\:of\:the\:line\:that's\:parallel\:to\:the\:given\:line: \dfrac{1}{3}}[/tex]
[tex]\textsf{Next, we'll apply the \textbf{Point-Slope Formula:}}[/tex]
[tex].\qquad\bullet\sf{y-y_1=m(x-x_1)}[/tex]
[tex]\textbf{\underline{Setting the values:}}[/tex]
[tex].\qquad\bullet\sf{y_1=2}\\.\qquad\bullet m=1/3\\.\qquad\bullet x_1=6}}[/tex]
[tex]\textbf{\underline{Plugging in the values:}}[/tex]
[tex].\qquad\bullet\sf{y-2=\dfrac{1}{3} (x-6)}\\\\.\qquad\bullet y-2=\dfrac{1}{3}x-2}\\\\.\qquad\bullet y=\dfrac{1}{3} x}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\large\overbrace{\underbrace{\textsf{\textbf{Reflection - RoSe}}}}^\star_\star[/tex]
of a number is 16. What is the number?
First, write an equation to describe the situation.
Answer: 40
Step-by-step explanation:
ok, so the unknown number is x
2/5(x)=16
multiply by the reciprocal, which is 5/2 to cancel out the 2/5
so your new equation is x=16*5/2
you should get 40
I am struggling with 6 2/5 revolutions in 2 2/3 seconds and turning it into a unit rate
[tex]\frac{12}{5}[/tex] = [tex]2\frac{2}{5}[/tex] revolutions per second is the unit rate.
What is unit rate ?An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
1) Convert mixed fractions into fractions.
[tex]6\frac{2}{5}[/tex] = [tex]\frac{((6*5) + 2)}{5}[/tex] = [tex]\frac{32}{5}[/tex]
[tex]2\frac{2}{3}[/tex] = [tex]\frac{((2*3) + 2)}{3}[/tex] = [tex]\frac{8}{3}[/tex]
2) [tex]\frac{32}{5}[/tex] ÷ [tex]\frac{8}{3}[/tex] ; where [tex]\frac{32}{5}[/tex] is the 1st fraction and [tex]\frac{8}{3}[/tex] is the 2nd fraction
a) Find the second fraction's reciprocal:
From [tex]\frac{8}{3}[/tex] to [tex]\frac{3}{8}[/tex]
b) Multiply the first fraction by the second fraction's reciprocal, which is 32/5, 5/3, or (5/3), to get 96/40.
c) Simplify the fraction.
Divide 96 / 40 by 4 to get 24/10.
Divide 24/10 by 2, and the result is 12/5. The 96/40 simple fraction
[tex]\frac{12}{5}[/tex] = [tex]2\frac{2}{5}[/tex] revolutions per second is the unit rate.
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Express your answer as a polynomial in standard form.
ƒ(x) = 2x² + 5x + 15
g(x) = -x + 5
Find: (fog)(x)
Answer:
2x² - 25x + 90
Step-by-step explanation:
→ Replace every x in 2x² + 5x + 15 with -x + 5
2 × ( -x + 5 )² + 5 ( -x + 5 ) + 15
→ Simplify
2 ( x² - 10x + 25 ) - 5x + 25 + 15
→ Expand
2x² - 20x + 50 - 5x + 40
→ Simplify
2x² -25x + 90
8x + 5 = 29; x = 3
how does that work?
Answer:
You substitute the x with the number.
8(3)+5=29 so 8*3 is 24 + 5 is 29
Step-by-step explanation:
Evaluate the quantity one third raised to the second power times one third raised to the zero power end quantity all raised to the second power. one over 81 one over 27 one over 243 one over nine
The required simplified value of the quantity is 1 / 81. Option A is correct.
Given that,
To determine the simplified value of the quantity one-third raised to the second power times one-third raised to the zero power end quantity all raised to the second power.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
According to the question,
= [(1 / 3)² + ( 1 / 3)⁰]²
Simplification,
= (1 / 3)²°²
= (1 / 3)⁴
= 1⁴ / 3⁴
= 1 / 81 (since 3⁴ = 81)
Thus, the required simplified value of the quantity is 1 / 81. Option A is correct.
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can you use the multiplication property of inequality to solve 8m>-1/10?can you use the division of property to solve -9/2 >3/2?explain your reasoning
a) Yes, by multiplying both sides by 1/8.
b) The inequality is false, thus, there is nothing to solve.
can you use the multiplication property of inequality to solve 8m>-1/10?Yes, you can.
There is a property that says that if you perform the same operation (multiplicating by 1/8 in this case) in both sides, then the truth value of the inequality does not change.
8m > -1/10
So, if we multiply both sides by 1/8, we will get:
8m/m > -1/(10*8)
m > -1/80
The inequality is solved.
can you use the division of property to solve -9/2 >3/2?There is nothing to really solve here, as you can see, the inequality says that a negative number is larger than a positive number, so the inequality is clearly false, and thus, there is nothing to solve.
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Necesito ayuda con este problema si no lo entiendes traducelo y ayudame me puedes explicar en español ya que lo entiendo
Answer:
F
Step-by-step explanation:
La respuesta es f porque la tasa vigente en el lado x es por 2 y la tasa vigente en el lado y es por 12.
Lin ordered 250 pens and 250 pencils to sell for a theatre club fundraiser. the pens cost 11 cents more than the pencils. if lin's total order costs $42.50, find the cost of each pen and pencil.
Using algebraic expression and equation, each pen costs 14 cents while each pencil costs 3 cents.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
Given that the pens cost 11 cents more than the pencils, we can express this as:
x = 11 + y
where x = cost of each pen (cents)
y = cost of each pencil (cents)
If Lin ordered 250 pens and 250 pencils and the total order costs $42.50, we can express that as:
250x + 250y = $42.50
Substitute the value of x in this equation and solve for y.
250x + 250y = $42.50
250(11 + y) + 250y = 4250 cents
2750 + 250y + 250y = 4250
500y = 1500
y = 3
cost of each pencil = 3 cents
x = 11 + y
x = 11 + 3
x = 14
cost of each pen = 14 cents
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A football was kicked vertically upward from a height of 4 feet
with an initial speed of 60 feet per second. The formula
h = 4 + 60t - 16t
2
describes the ball’s height above the ground, h, in feet, t seconds
after it was kicked. Use this formula to solve Exercises 19–20.
19. What was the ball’s height 2 seconds after it was kicked?
Answer: h=60 feet
Step-by-step explanation:
h=4+60t-16t²
h(2)=4+(60)(2)-(16)(2)²
h(2)=4+120-(16)(2)(2)
h(2)=124-64
h(2)=60 feet
Write an equation for each line. m=0 and the y -intercept is (0,-2) .
The equation of a line with slope = 0 and y-intercept = (0,-2) is: y = -2
What is the equation of a line to the curve?A line's equation has the standard form ax + by + c = 0. Here, the variables are x and y, the coefficients are a and b, and the constant term is c.It is a first-order equation with the variables x and y.The coordinates of the point on the line shown in the coordinate plane are represented by the values of x and y.Now,
Given:
Slope of the given line = 0Coordinates of the y-intercept = (0,-2)To find: Equation of the line
Finding:
Now, we know that the slope-point form method to find the equation of a line, requires only two things: slope of the line and coordinates of the y-intercept.
The equation so given by the method: y = mx + c, where
m = slope of the line
c = y-intercept
On substituting the given values in the above equation, we get:
=> y = 0x - 2, which the required equation of the line.
Hence, The equation of a line with slope = 0 and y-intercept = (0,-2) is: y = -2.
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A
hippopotamus
lost 400 pounds over 8 months. What is the
's average change in weight per month?
Answer:50 pounds a month
Step-by-step explanation:400 divided by 8=50pounds
Line MS is perpendicular to line OP. If M(-6,8), O(k+3,-20), P(13,k-2) and S(-2,5) find k
The value of the variable k must equal to - 2 such that the line segment MS is perpendicular to the line segment OP.
What is the value of a variable associated with line segments perpendicular to each other?
According to analytical geometry, two lines are perpendicular to each other if the product of their slopes are equal to - 1. Slopes can be determine by secant line formula:
m₁ = (5 - 8) / [- 2 - (- 6)]
m₁ = - 3 / 4
m₂ = [(k - 2) - (- 20)] / [13 - (k + 3)]
m₂ = (k + 18) / (10 - k)
(- 3 / 4) · [(k + 18) / (10 - k)] = - 1
(- 3 / 4) · (k + 18) = - (10 - k)
- 3 · (k + 18) = - 4 · (10 - k)
- 3 · k - 54 = - 40 + 4 · k
7 · k = - 54 + 40
7 · k = - 14
k = - 2
The value of the variable k must equal to - 2 such that the line segment MS is perpendicular to the line segment OP.
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Why does -3.6 -(-4) have the same result as -3.6 + 4?
find the equation of the line shown
Write the specified type of proof.
two-column proof
Given: CB bisects ∠A B D and ∠A C D .
Prove: Δ A B C ≅ ΔD B C
ΔABC ≅ ΔDBC under angle-side-angle (ASA) condition.
What precisely is meant by a triangle's congruency?Two triangles are considered to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be decided to move, rotated, flipped, and turned to appear identical.If they are repositioned, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
To prove: ΔABC ≅ ΔDBC
BC = BC = (common:given)∠BCA = BCD = (Given: CB bisects ∠C)∠CBA = CBD = (Given: CB bisects ∠B)Then, ΔABC ≅ ΔDBC under angle-side-angle (ASA) condition.
(Refer the table shown below)
Therefore, ΔABC ≅ ΔDBC under angle-side-angle (ASA) condition.
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100 POINTS + MARKING BRAINLEIST
Triangle DEF was rotated 90 degrees about the origin to form congruent triangle LMN. Hence, EF ≅ MN.
What are congruent triangles?Two triangles are said to be congruent if they have the same shape and their corresponding sides are also equal. Therefore, their corresponding angles would also be congruent.
Rotation, reflection and translation produces congruent triangles.
Hence:
Triangle DEF was rotated 90 degrees about the origin to form congruent triangle LMN. Hence, EF ≅ MN.
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A salad dressing is made by mixing lemon juice and vinegar in the ratio 4:3 Vicky makes 700 ml of the salad dressing. How much lemon juice does she use? Give your answer in millilitres (ml).
Answer:
400 ml of lemon juice
Step-by-step explanation:
We know that there are 700 ml of salad dressing, and the ratio of lemon juice to vinegar is 4:3. We know that therefore, there are 7 equal parts. To find how many ml are in one part, we divide 700 by 7, which gives us 100. Then we can multiply that answer by 4 to find how many ml of lemon juice and 3 to find how many ml of vinegar.
100 x 4 = 400
Therefore, Vicky uses 400 ml of lemon juice.
Pls pls help whoever gets it right gets a crown
A shop owner sold 27 books on Friday. This was 9 more than the number of books he sold on Thursday. Identify an equation and its solution that shows the number of books he sold on Thursday.
x − 9 = 27; 36 books
x + 27 = 36; 9 books
x + 9 = 27; 18 books
9x = 27; 3 books
The expression that shows the number of books he sold on Thursday is x + 9 = 27; 18 books
How to determine the equation and the solution?The given parameters are
Friday sales = 27
Friday sales = 9 more than the number of books he sold on Thursday.
Let the number of books he sold on Thursday be x
So, we have
Friday = 9 + x
This gives
27 = 9 + x
Rewrite as
x + 9 = 27
Solve
x = 18
Hence, the expression that shows the number of books he sold on Thursday is x + 9 = 27; 18 books
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How do I solve this equation 3.2x+12=48
Answer:11.25
Step-by-step explanation: first subtract 12 from both sides then you would have 3.2x=36
and then divide both sides by 3.2 which is x=11.25
Answer: x=11.25
Step-by-step explanation: 48-12> 36> 3.2x=36> divide 36 by 3.2> x= 11.25
Hope this helped
