Answer:
x = -3/2
Step-by-step explanation:
x + 3 + d = 2x + 1 First term plus common difference = 2nd term
x -2 = d
x + 3 + 2d = 5x+2 First term + 2 d = third term re-arrange:
4x-1 = 2d sub in the definition of d from above
4x -1 = 2 (x-2)
4x-1 = 2x-4
2x = -3
x = -3/2
If x+3, 2x+1, and 5x+2 are consecutive terms of an arithmetic sequence then x is -3/2.
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The sequence in which consecutive terms will have common difference is called as Arithmetic sequence.
x+3, 2x+1, and 5x+2
The common difference between first term and second term
d=2x+1-x-3
d=x-2
The common difference between second term and third term
5x+2-2x-1=d
3x+1=d
Now plug in d value
3x+1=x-2
Subtract x from both sides
3x-x=-3
2x=-3
Divide both sides by 2
x=-3/2
Hence, if x+3, 2x+1, and 5x+2 are consecutive terms of an arithmetic sequence then x is -3/2.
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9 yd
6 yd
8 yd
Volume of the pyramid
Answer:
Volume = 144
V = length(9) × width(6) × height(8) ÷ 3 = 144
What number am i?7 times two digit number equals 4 times number with the digit reversed .the sum of the digits is 3.
Answer:
12
Step-by-step explanation:
7 times 12 is 84. 4 times 21 is 84. The digits have a sum of 3.
If f(x) = 16x^2 – 20x, what is the value of f(3)?
(Pls show work)
Answer:
f(3) = 84
Step-by-step explanation:
To evaluate a function for a specific value of the variable, put the value in the function's expression where the variable is, and do the arithmetic.
__
Sometimes it works well to simplify the expression a bit.
f(x) = 16x^2 -20x = 4x(4x -5)
f(3) = 4(3)(4(3) -5)) = (12)(7)
f(3) = 84
Which THREE statements would produce the truth value F when pis true and q is false?
The THREE statements that would produce the truth value F when p is true and q is false are (a) p → q (b) ¬ p ∧ ¬ q (d) q ∨ ¬ p
How to determine the statements with a false truth value?To do this, we simply analyze each option
The given parameters are:
p = true
q = false
(a) p → q
This means that:
If p then q
So, we have:
If true then false
The above statement would return false.
(b) ¬ p ∧ ¬ q
This means that:
If not p and not q
So, we have:
If not true and not false
i.e.
If false and true
The above statement would return false.
(c) p → ¬ q
This means that:
If p then not q
So, we have:
If true then not false
i.e.
If true then true
The above statement would return true.
(d) q ∨ ¬ p
This means that:
If q and not p
So, we have:
If false and not true
i.e.
If false and false
The above statement would return false.
Hence, the THREE statements that would produce the truth value F when p is true and q is false are (a) p → q (b) ¬ p ∧ ¬ q (d) q ∨ ¬ p
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The equation 6 = 2x2 – 11x has two solutions, p and q, with p being greater than q.
What is the value of p – q?
[tex]~~~~~~6=2x^2 -11x\\\\\implies 2x^2 -11x -6 = 0\\\\\implies 2x^2 -12x +x-6=0\\\\\implies 2x(x-6) +(x-6) = 0\\\\\implies (2x+1)(x-6) = 0\\\\\implies x = -\dfrac 12,~~ x= 6\\\\\text{Since }~p > q,}~~ p =6~ \text{and}~ q = -\dfrac 12\\ \\\text{So,}~ p-q = 6 -\left(- \dfrac 12 \right)\\\\~~~~~~~~~~~~~=6+\dfrac 12 \\\\~~~~~~~~~~~~~=\dfrac{13}2\\\\~~~~~~~~~~~~~=6.5[/tex]
The value of p -q is 6.5.
How to find the roots of a quadratic equation?Suppose that the given quadratic equation is
ax^2 + bx + c = 0
Then its roots are given as:
[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
The equation 6 = 2x^2 - 11x has two solutions, p and q, with p being greater than q.
[tex]6 = 2x^2 - 11x \\\\ 2x^2 - 11x - 6 = 0\\\\ 2x^2 - 12x + x- 6 = 0\\[/tex]
(2x + 1) (x-6) = 0
Thus, x = -1/2 , 6
Since p>q
p = 6 , q = -1/2
So, p -q = 6 - (-1/2)
= 6 + 1/2
= 13/2
= 6.5
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Select the correct answer. what is the simplest form of this expression? (x 7)(3x − 8) a. 3x2 2x − 15 b. 3x2 29x − 1 c. 3x2 − 29x − 56 d. 3x2 13x – 56
The simplest form of the expression (x + 7)(3x − 8) is 3x² + 13x - 56
How to determine the simplest form of this expression?The expression is given as:
(x + 7)(3x − 8)
Expand the expression
3x² - 8x + 21x - 56
Evaluate the like terms
3x² + 13x - 56
Hence, the simplest form of the expression (x + 7)(3x − 8) is 3x² + 13x - 56
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2. Noah is solving the equation x² + 8x + 15 = 3. He begins by rewriting the
expression on the left in factored form and writes (x + 3)(x + 5) = 3. He
does not know what to do next.
Noah knows that the solutions are x = -2 and x = -6, but is not sure how
get to these values from his equation.
Solve the original equation by completing the square.
Answer:
The solution set is {-6, -2}.
Step-by-step explanation:
x^2 + 8x + 15 = 3
x^2 + 8x = -12
Completing the square:
(x + 4)^2 - 16 = -12
(x + 4)^2 = 4
Taking square roots of both sides:
x + 4 = +/- 2
x = 2 - 4 = -2 or x = -2-4 = -6.
will give brainliest
Answer:
Here is your answer
Step-by-step explanation:
Bearing from point A to B, can be calculated as,
beta = atan * 2(X, Y)
where, X and Y are two quantities and can be calculated as:
X=cos theta b^ * s AL
Y=cos theta a^ * sin theta b-sin theta a^ * cos theta b^ * cos Delta l put the values and calculate
Vertical angles are congruent. Find the measure of angle x. X 38 o x = = [?]
Answer:
x=38 degrees
Step-by-step explanation:
Vertical angles are congruent. In the image, angle x is vertical to the angle that is given. Therefore, x=38 degrees
Awnser This Question to get 10pts!
Remember to say: 1. 2. (Beetween 1.) and 3.
Answer
Box (1) : 240Box (2) : 40Box (3) : 2632Hope it helps
A tangent PQ at a point P of a circle of radius. 5cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :
A)12 cm
B) 13 cm
C) 8.5 cm
D) √119 cm
Answer :
[tex]\boxed{D) \sqrt{119} \: cm}[/tex]
Solution :
In the above figure, the line that is drawn from the centre of the given circle to the targent PQ is perpendicular to PQ.
And So, OP ⊥ PQ
Using Pythagoras theorem in triangle ΔOPQ we get ,
[tex]\Longrightarrow\: OQ^2 = OP^2 + PQ^2[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\: (12)^2 = 5^2+PQ^2[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\: PQ^2 = 144-25[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\: PQ^2 = 119[/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\: PQ = \sqrt{119} [/tex]
[tex]\: \: \: \: \: \: \: \: \: \: \: \: [/tex]
So, option D) √119 cm is the length of PQ.
what’s -12/2 simplified
Answer:
= -6
Step-by-step explanation:
-12/2
= -6
How do you find area of a figure ?
Length × Width = Area
Answer:
The length x the widith. If there's more then 4 sides I think you just multiply them all together
Step-by-step explanation:
I need help for this one!!! What u
The above is not a function because -2 is mapped to two elements 2 and -4.
What is a function?A function relates an input to an output. The three main parts of a function are the inputs, outputs and the relationship.
The formal definition of a function is that it relates each element of a set with exactly one element of another set (possibly the same set).
In other words, one element must be mapped to another element.
Each element cannot be mapped to two elements.
Therefore, the above is not a function.
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What is the common difference between successive terms in the sequence? 2, 8, 14, 20, 26,. –6 –4 4 6.
Answer:
The common difference is the difference between any two consecutive terms in an arithmetic sequence.
The formula which is used to find the common difference in AP is
d = an - an-1
Here the common difference is
d = a2 - a1 = 8 - 2 = 6
d = a3 - a2 = 14 - 8 = 6
d = a4 - a3 = 20 - 14 = 6
d = a5 - a4 = 26 - 20 = 6
2, 8, 14, 20, 26 … = 2, (2 + 6), (8 + 6), (14 + 6), (20+ 6) …
Therefore, the common difference is 6.
Step-by-step explanation:
The points (−8,−2) and (7,4) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
Answer
8.08
Use the distance formula:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
where (x1, y1), (x2, y1) are points
[tex]\rightarrow \sf d =\sqrt{(7-(-8))^2 + (4-(-2))^2}[/tex]
[tex]\rightarrow \sf d =\sqrt{(15)^2 + (6)^2}[/tex]
[tex]\rightarrow \sf d =3\sqrt{29}[/tex]
This is the length of diameter.
Then radius:
· diameter/2
[tex]\sf \cdot \dfrac{3\sqrt{29} }{2}[/tex]
[tex]\sf \cdot 8.0777[/tex]
[tex]\sf \cdot 8.08 \ \ (rounded \ to \ nearest \ hundreth)[/tex]
Hcf of 520 and 1430 pls i want to check my answer
Answer: HCF=130
Step-by-step explanation:
Select the correct answer from the drop-down menu. a survey conducted in a certain town found that 1 out of every 5 individuals owned a bike. a statistician calculated the margin of error to be 1.5%. the maximum percentage of individuals who own a bike is .
The maximum percentage of individuals who own a bike is 21.5%.
What is the maximum percentage?Margin of error is the percentage points a researcher's value would differ from the real population's value. The maximum percentage is the sum of the margin of error and the true value.
The maximum percentage = margin of error + true value
(1/5) x 100 + 1.5% = 21.5%
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Answer:
See image
Step-by-step explanation:
Plato
HELPPPP
y=1/8x+3 in standard form
Answer:
[tex]x-8y=-24[/tex]
Step-by-step explanation:
Standard form of a linear equation: [tex]Ax+By=C[/tex]
(where A, B and C are integers, and A shouldn't be negative)
Given equation:
[tex]y=\dfrac{1}{8}x+3[/tex]
Multiply both sides by 8:
[tex]\implies 8 \cdot y=8 \cdot \dfrac{1}{8}x+8 \cdot 3[/tex]
[tex]\implies 8y=x+24[/tex]
Subtract 8y from both sides:
[tex]\implies 8y-8y=x+24-8y[/tex]
[tex]\implies 0=x+24-8y[/tex]
Subtract 24 from both sides:
[tex]\implies 0-24=x+24-8y-24[/tex]
[tex]\implies -24=x-8y[/tex]
In standard form:
[tex]\implies x-8y=-24[/tex]
109, 94, 87, 103, 89, 112, 98, 115, 99 Find the minimum.
ANSWER ASAP PLEASE
Answer:
The minimum is 87
Step-by-step explanation:
The minimum is the lowest number that you can see. 87 is the minimum because it is the lowest of all numbers listed
Answer:
87
Step-by-step explanation:
Put them in order
87, 89, 94, 98, 99, 103, 109, 112, 115
Minimum = The least
The least = 87
A marketing executive earns an annual salary of $78,300, and she contributes $6,500 per year to her 401(k) plan. If she has a required deduction for income taxes (federal, state, and local combined) of 27% of pretax income, how much is withheld in income taxes per year?
Answer:
With the assumption being made that the 401-k deductions are pre-tax deductions your calculation is as follows:78,300 - 6,500 = 71,800 (this is your new taxable value)71,800 * 0.27 = 19,386 (This is the amount that will be withheld in income taxes per year.Your answer is A.
Answer:
Step-by-step explanation:
With the assumption being made that the 401-k deductions are pre-tax deductions your calculation is as follows:
78,300 - 6,500 = 71,800 (this is your new taxable value)
71,800 * 0.27 = 19,386 (This is the amount that will be withheld in income taxes per year.
Simplify the expression (2x − 9)(x 6). a. 2x2 − 54 b. 2x2 − 3x − 54 c. 2x2 3x − 54 d. 2x2 21x − 54
The means of simplifiying is by factoring. The simplified form of the expression is 2x² + 3x - 5
Simplifying expressionsThe means of simplifiying is by factoring
Given the expression
(2x - 9) (x+ 6)
Expand
(2x - 9) (x+ 6)
2x² +12x -9x - 54
2x² + 3x - 54
Hence the simplified form of the expression is 2x² + 3x - 54
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Answer: It's
c
Step-by-step explanation:
What is 8.92 cm² Converted To Meters?
[tex]8.92 ~ \text{cm}^2\\\\=8.92 \times \left( 1 ~ \text{cm} \right)^2\\\\=8.92 \times \left(10^{-2}~ \text{m} \right)^2~~~~~~;\left[1~ \text{cm} = \dfrac{1}{100}~ \text m} = 10^{-2}~ \text{ m} \right]\\\\=8.92 \times 10^{-4}~ \text{m}^2\\\\=0.000892~ \text{m}^2[/tex]
In a company's first year in operation, it made an annual profit of $140,000. The profit of the company increased at a constant 20% per year each year. How much total profit would the company make over the course of its first 14 years of operation, to the nearest whole number?
Answer:
$8,287,429
Step-by-step explanation:
The total profit will be the sum of a geometric series. The formula for that sum is ...
Sn = a1 × (r^n -1)/(r -1)
where a1 is the first term, r is the common ratio, and n is the number of terms.
__
Here, the series has first term $140,000, common ratio 1+0.20 = 1.2, and we want the total of 14 terms. The total profit is ...
S14 = ($140,000) × (1.2^14 -1)/(1.2 -1) ≈ $8,287,429
In the first 14 years of operation, the total profit would be $8,287,429.
Are the ratios 4:8 and 1:2 equivalent?
Answer:
yes
Step-by-step explanation:
yes they are i can see this because, 4/8 is the same as 1/2.
I know this because if you reduce 4/8, you will get 1/2.
11 x_
= 121 what is the missing number?
Answer:
11
Step-by-step explanation:
11x=121
11x/11 = 121/11
x = 11
So, 11*11 = 121
The rule is "Star, Circle, Heart."What is the
17th shape?
Answer:
Circle
Step-by-step explanation:
The Breaker's Manufacturing Company makes 80% of a particular sensor, the Cartin Company makes 15% of them, and the Flutes Company makes the other 5%. The sensors made by Breaker's have a 4% defect rate, the Cartin sensors have a 6% defect rate, and the Flutes sensors have a 9% defect rate. If a sensor is randomly selected from the general population of all sensors, what is the probability that it is defective, given that it was made by Breaker’s?
Answer:
0.04
Step-by-step explanation:
The sensors made by Breaker's have a 4% defect rate
Identifying the Graph of a
Function
Try It
Which graph represents the function h(x) = |x - 3|?
Answer: the one that passes through the y-intercept of -3
Step-by-step explanation:
Answer:
its c
Step-by-step explanation:
What is the distance between the points X(−4,3) and Y(2,−7) rounded to the nearest tenth?
Step-by-step explanation:
first, draw a graph and subtract the nbers in brackets with the others. when done -6,-4 will help you solve the answer
The distance between the points X(−4,3) and Y(2,−7) rounded to the nearest tenth is 11.7 units
Distance between two pointsThe formula for calculating the distance between two points is expressed as:
D = √(y2-y1)²+(x2-x1)²
Given the coordinate points X(−4,3) and Y(2,−7)
Substitute
XY = √(-7-3)²+(2+4)²
XY = √(-10)²+(6)²
XY = √100+36
XY = √136
XY = 11.7 units
Hence the distance between the points X(−4,3) and Y(2,−7) rounded to the nearest tenth is 11.7 units
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