Let a be the first term and d the common difference between consecutive terms. Then the next few terms in the sequence are
a + d
a + 2d
a + 3d
and so on, up to the k-th term
a + (k - 1) d
The sum of the first n terms of this sequence is
[tex]\displaystyle S_n = \sum_{k=1}^n(a+(k-1)d) = 12n-2n^2[/tex]
Expanding the sum, we have
[tex]\displaystyle S_n = \sum_{k=1}^n (a+(k-1)d) \\\\ S_n = \sum_{k=1}^n(a-d+dk) \\\\ S_n = (a-d)\sum_{k=1}^n1+d\sum_{k=1}^nk \\\\ S_n = (a-d)n+\frac{d}2n(n+1) \\\\ S_n = (a-d)n+\frac{d}2(n^2+n) \\\\ S_n = \left(a-\frac{d}2\right)n+\frac{d}2n^2[/tex]
It follows that
a - d/2 = 12
d/2 = -2
Solve these equations for a and d.
d/2 = -2 ==> d = -4
a - d/2 = a + 2 = 12 ==> a = 10
So the sequence is
10, 6, 2, -2, -6, -10, -14, …
One car travels 390 miles in the same amount of time it takes a second car traveling 3 miles per hour slower than
the first to go 372 miles. What are the speeds of the cars?
The speed of the cars are
miles per hour.
Translate this phrase into an algebraic expression.
61 less than twice Jenny's age
Use the variable j to represent Jenny's age.
The tree diagram represents an experiment consisting of two trials. P(c)=
Answer:
0.8
Step-by-step explanation:
To get to C, you must start by taking the lower of the first two branches
That has a probability of 0.4
C is the branch on your right and has a probability of 0.2
P(C) = 0.4 * 0.2 = 0.8
Answer:
.26
Step-by-step explanation:
Find the missing side length. Leave your answers radical in simplest form. PLEASE HURRY
Answer:
the answer for y is 9 and x is 9✔2( the check is square root symbol)
A boat can travel 21 miles on 7 gallons of gasoline. How far can it travel on 17 gallons?
Answer:
51 miles
Step-by-step explanation:
Boat with 7 gallons of gas = 21 miles
Boat with 1 gallon of gas = 21/7 = 3 miles
Boat with 17 gallons of gas = 17 x 3 = 51 miles
Answer:
51 miles
Step-by-step explanation:
1 gallon = 3 miles
17 gallons = ? miles
17 * 3 = 51 miles
What is the solution to 4x + 2 = 6(-2x - 5) ?
Group of answer choices
16
2
-16
-2
Answer:
x= -2
Step-by-step explanation:
4x + 2 = 6(-2x - 5)
Distribute
4x+2 = -12x-30
Add 12x to each side
4x+2+12x = -12x-30+12x
16x+2 = -30
Subtract 2 from each side
16x+2-2=-30-2
16x = -32
Divide by 16
16x/16x = -32/16
x = -2
How much would $150 invested at 8% interest compounded continuously be worth after 17 years? Round your answer to the nearest cent.
A(t)= P•e^rt
A. $471.39
B. $555.00
C. $354.00
D. $584.43
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Answer:
D. $584.43
Step-by-step explanation:
Using the given formula with the given values, we find ...
A(17) = 150·e^(0.08·17) = 584.43
find the length of the arc. round your answer to nearest tenth
41.9 mi
Step-by-step explanation:
First, we convert the angle from degree measure to radian measure:
[tex]\theta = 240°×\left(\dfrac{\pi}{180°}\right)= \dfrac{4\pi}{3}\:\text{rad}[/tex]
Using the definition of an arc length [tex]s[/tex]
[tex]s = r\theta[/tex]
[tex]\:\:\:\:=(10\:\text{mi})\left(\dfrac{4\pi}{3}\:\text{rad}\right)[/tex]
[tex]\:\:\:\:= 41.9\:\text{mi}[/tex]
5. Given a test in which there is overlap of the test results for diseased and non-diseased individuals (e.g., normal individuals are found who have test results ranging in value from 8 to 15, and diseased individuals are found who have test results ranging in value from 12 to 25, so that in the range of values 12 to 15 there are both normal and diseased individuals), if the current cutoff value lies in the range of this overlap and you move the cutoff value toward the normal population (lower numbers in this example), the true negative numbers will _____________________ . (5 points)
Answer:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase
Step-by-step explanation:
True negative numbers are considered as diseased individual. So, the true negative numbers will increase.
urgent !!!! HELP NEEDED
Answer:
[tex]352\ yd^2[/tex]
Step-by-step explanation:
1. Approach
The surface area of a three-dimensional figure is the two-dimensional space around the figure. Simply put, if one was going to wrap the figure up in paper, the surface area is the amount of paper one would need to wrap the entirety of the figure. One can find the surface area of a figure by finding the area of each individual facet of the figure and then adding up the areas.
2. Finding the area of the triangular faces
The formula to find the area of a triangle is the following:
[tex]A_t=\frac{b*h}{2}[/tex]
Where (b) is the base of the figure, and (h) is the figure's height. Since there is only one type of triangular face, one only has to find the area of one triangular face and then multiply its measurement by four.
Triangle 1
[tex]A_t=\frac{b*h}{2}[/tex]
[tex]A_t=\frac{11*10.5}{2}[/tex]
[tex]A_1=\frac{115.5}{2}[/tex]
[tex]A_t=57.75[/tex]
3. Finding the area of the quadrilateral
The following formula can be used to find the area of a quadrilateral:
[tex]A_q=b*h[/tex]
Substitute the dimensions of the quadrilateral in and solve for its area:
[tex]A_q=b*h[/tex]
[tex]A_q=11*11[/tex]
[tex]A_q=121[/tex]
4. Find the total surface area of the figure
To find the total surface area of the figure, add up all of the area values of its faces. Remember the area of the triangular face is multiplied by four because there are four triangular faces.
[tex]4(A_t)+(A_q)=A[/tex]
[tex]4(57.75)+121=A[/tex]
[tex]231+121=A[/tex]
[tex]352=A[/tex]
In the figure alongside, show that angle(a+b+c+d) = 4 right angles
Answer:
Proved
Step-by-step explanation:
a=180-x
c=a= 180-x
d=180-a = 180-(180-x) =x
b=d=x
adding every angle;
a+b+c+d= 180-x + x + 180-x + x
a+b+c+d = 180+180 = 360
a+b+c+d = 4 *90
The sum of the interior of the quadilateral is equal to 4 right angles.
The point where two lines meet is known as an angle
The given figure is a quadrilateral.
For the quadrilateral
The sum of opposite angles is 180degreesThe sum of all the interior angles is 360degreesAccording to the theorem;
a + c = 180 ...... 1
b + d = 180 ...... 2
Add both equations
a + b + c + d = 180 + 180
a + b + c + d = 360
Note that 1 right angle = 90degrees
4 right angles = 4(90) = 360 degrees
Therefore a + b + c + d = 4 right angles (Proved)
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help giving brainilest, heart, and 5 stars
Answer:
4 = 6
5 = -17
Step-by-step explanation:
4. a² - b / b² - c
a² = 2² = 4
b = -2
4 - (-2) = 4 + 2 = 6
6 / b² - c = 6/4 - 3 = 6/1 = 6
4 = 6
5. -3x² + 2xy + 7
-3x² = -3 * -2² = -3 * 4 = -12
2xy = 2 * -2 * 3 = -4 * 3 = -12
-12 + -12 + 7 = -24 + 7 = -17
5 = -17
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Help me with this please.
Answer:
the answer should be B
Step-by-step explanation:
take the total of people who got the flu(63) and the amount of them who were vaccinated(35) and write it as a fraction. 35/63 in its simplest form is 5/9
f(x) = 2x3 + 7x2 – 4x – 5
g(x) = 3x – 2
Find (f - g)(x).
A. (f - g)(x) = 2x3 + 7x2 – 2 – 3
O B. (f – g)(x) = 2x3 + 7x2 – 2 – 7
O C. (f - g)(x) = 2x3 + 7m2 – 72 – 3
O D. (f - g)(x) = 2x3 + 7x2 – 73 – 7
Answer:
A. 6
B. 2
C. 8
D. 3
all the answers to the previous questions
D.) = 3
The value of the function (f -g)(x) will be 2x^3 + 7x^2 - 7x - 3
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable, Linear function is a function whose graph is a straight line
We are given that the function as;
[tex]f(x) = 2x^3 + 7x^2 - 4x - 5[/tex]
[tex]g(x) = 3x - 2[/tex]
We need to find the function as (f - g)(x)
(f -g)(x) = f(x) -g(x)
(f -g)(x) = 2x^3 + 7x^2 - 4x - 5 - 3x + 2
(f -g)(x) = 2x^3 + 7x^2 - 7x - 3
Therefore, the correct option is C 2x^3 + 7x^2 - 7x - 3
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5 Cece draws these two figures to prove there is more
than one parallelogram with a 40° angle between a
2-cm side and a 6-cm side. Is Cece correct? Explain.
2 cm
40
4.
2 cm
Answer:
chash greatly ta 45uerywryrsyrsyrs
you decide to go to technical school for 2 years to get a degreee in computer networking. it takes you 8 quarters to complete the program abd it costs $830 per quarter for tuition in addition to books for the programs that cost 1800 how much will is cost you to get your degree
whats the answer
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Answer:
$8440
Step-by-step explanation:
8 quarters at $830 per quarter is 8×$830 = $6640.
When the cost of books is added, the total is ...
$6640 +1800 = $8440
Please please help!! Quickly
Answer:
pretty sure its D
Answer:
I have to give 2 Ans for my question
40pts and a brainliest to the person who can help me with this stock problem. PLEASE show all steps in detail so I can learn how to do this!
What is the rate of return when 20 shares of Stock A, purchased for $30/share, are sold for $710? The commission on the sale is $6. Give your answer as a percent rounded to the nearest tenth.
Answer:
Rate of Return is 14.8%
Step-by-step explanation:
We know that 20 shares of Stock are purchased for $30 per share.
This gives us a total value of: 20 × 30 = $600.
Now, the shares are sold for $710 with a commission sale of $6. This means the final money going to the seller is; 710 – 6 = $704.
Thus, the rate of return percentage is = (704 – 600)/704) × 100% = 14.7727%
To the nearest tenth gives us 14.8%
Which compound inequality does the number line represent?
ILL MAKE BRAINLIEST PLEASE HELP
The compound ineqality which the number line represents will be 5x ≥ -15 or 5x ≤ 10 so option (B) must be correct.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
A mathematical expression is said to be unequal if the sides are not equal. Essentially, comparing any two values shows whether one is smaller, greater, or equal to the value on the other side of the equation.
In option (B) given that
5x ≥ -15
⇒ x ≥ -15/5
⇒ x ≥ -3
And
5x ≤ 10
⇒ x ≤ 10/5
⇒ x ≤ 2
By looking at the number line it is clear that the blue line is greater than -3 and less than 2 hence it will be correct.
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Rectangle TUVW is dilated by a scale factor of 3
3 to form rectangle T'U'V'W'. Side U'V' measures 93
93. What is the measure of side UV?
Answer:
31
Step-by-step explanation:
93/3=31
So UV is equal to 31
Answer:
31
Step-by-step explanation:
Points A(p,6), B(-3,q) and C(r,8) are on a line whose equation is y=-2x+3. How find the unknown coordinates of A,B, and C?
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Answer:
p = -3/2q = 9r = -5/2Step-by-step explanation:
Put the given coordinates in the equation for the line and solve for the unknown.
y = -2x +3
(p, 6) ⇒ 6 = -2p +3 ⇒ p = -3/2
(-3, q) ⇒ q = -2(-3) +3 ⇒ q = 9
(r, 8) ⇒ 8 = -2r +3 ⇒ r = -5/2
why infinity ( ) can’t be included in an inequality?
Answer:
Step-by-step explanation:
Because then the value on the other side will be unbounded by the infinity sign while expressing the answers on a number line.
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Write six hundred twelve thousand, three hundred in the place-value chart. Then write the number in expanded
Answer:
612,300
600,000
10,000
2,000
300
00
0
A store is advertising a new DVD player for $189.00. If the sales tax rate is 7.25 percent,
Answer:
then what's the question???..
To find the distance AB across a river, a distance BC of 415 m is laid off on one side of the river. It is found that B = 112.2° and C = 18.3°. Find AB.
Answer:
AB or the distance across the river is about 171.36 meters.
Step-by-step explanation:
Please refer to the diagram below (not to scale). The area between the two blue lines is the river.
To find AB, we can use the Law of Sines. Recall that:
[tex]\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}[/tex]
BC (or a) is opposite to ∠A and AB (or c) is opposite to ∠C. Thus, we will substitute in these values.
First, find ∠A. The interior angles of a triangle must total 180°. Thus:
[tex]m\angle A + m\angle B + m\angle C = 180^\circ[/tex]
Substitute:
[tex]\displaystyle m\angle A + (112.2^\circ) +(18.3^\circ) = 180^\circ[/tex]
Solve for ∠A:
[tex]m\angle A = 49.5^\circ[/tex]
Substitute BC for a, AB for c, 49.5° for A and 18.3° for C into the Law of Sines. Thus:
[tex]\displaystyle \frac{\sin 49.5^\circ}{BC} = \frac{\sin 18.3^\circ}{AB}[/tex]
Since BC = 415 m:
[tex]\displaystyle \frac{\sin 49.5^\circ}{415} = \frac{\sin 18.3^\circ}{AB}[/tex]
Solve for AB. Cross-multiply:
[tex]\displaystyle AB \sin 49.5^\circ = 415\sin 18.3^\circ[/tex]
And divide:
[tex]\displaystyle AB = \frac{415\sin 18.3^\circ}{\sin 49.5^\circ}[/tex]
Use a calculator. Hence:
[tex]AB = 171.3648...\approx 171.36\text{ m}[/tex]
AB or the distance across the river is about 171.36 meters.
8x-5/6x
Find all real numbers for which the rational expression is undefined
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Answer:
as written: noneperhaps intended: 0Step-by-step explanation:
The expression written here is interpreted according to the Order of Operations as ...
8x -(5/6)x
This reduces to (7 1/6)x, which is defined for all real numbers.
__
Maybe you intended the expression ...
(8x -5)/(6x)
This expression is undefined where its denominator is zero, at x = 0.
Graph the function f(x)=x^2+2x-8
what are x intercepts
what are y intercepts
what is maximum or minimum value
Answer:
The x intercepts are 2, -4
The y intercept is -8
The minimum is -9
Step-by-step explanation:
f(x)=x^2+2x-8
To find the x intercepts, set equal to zero and factor
0 =x^2+2x-8
0 = (x+4)(x-2)
Using the zero product property
0 = x+4 0 = x-2
x = -4 x = 2
The x intercepts are 2, -4
To find the y intercepts, set x =0 and solve for y
y = 0^2 +2(0) -8
y = -8
The y intercept is -8
Since the coefficient of the x^2 is positive, the parabola opens up so we have a minimum.
The vertex is halfway between the x intercepts
(-4+2)/2 = -2/2 = -1
To find the minimum substitute x= -1 into the equation
f(x)=x^2+2x-8
f(-1) = (-1)^2 +2(-1)-8 = 1-2-8 = -9
The minimum is -9
Graph attached
y=x²+2x-8y=x²+4x-2x-8y=x(x+4)-2(x+4)y=(x+4)(x-2)x intercepts (-4,0) and (2,0)
Y intercept :-
Put x=0
y=-8(0,-8)
Vertex is the minimum
(-1,-9)The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00. Write a function to represent this scenario.
Which graph represents this wage increase for x < 12?
Answer:
bhlhgewafhjffdgnhgreesdbjitbbbbhbfghjkkbiiuuhhh3C - 2/7 -5c-8/4=1/14
(2+1/2) (2^2-1+1/4) find the expression in the form of cubes and differences of two terms.
Answer:
Consider the following identity:
a³ - b³ = (a + b)(a² - ab + b²)Let a = 2, b = 1/2
(2 + 1/2)(2² - 2*1/2 + 1/2²) = 2³ - (1/2)³ =8 - 1/8Use the algebraic identity given below
[tex]\boxed{\sf a^3-b^3=(a+b)(a^2-ab+b^2)}[/tex]
[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-1+\dfrac{1}{4})[/tex]
[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-2\times \dfrac{1}{2}+\dfrac{1}{2}^2)[/tex]
Here a =2 and b=1/2[tex]\\ \sf\longmapsto 2^3-\dfrac{1}{2}^3[/tex]
[tex]\\ \sf\longmapsto 8-\dfrac{1}{8}[/tex]
