Choose the correct answer from the given four options: In an AP, if d = –4, n = 7, an = 4, then a is *

6

20

7

28​

Answers

Answer 1

[tex]a = 28.[/tex]

Step-by-step explanation:

[tex] {a}n = a + (n - 1)d[/tex]

[tex]4 = a + (7 - 1)( - 4)[/tex]

[tex]4 = a + 6( - 4)[/tex]

[tex]4 = a + ( - 24)[/tex]

[tex]4 = a - 24[/tex]

[tex]4 + 24 = a[/tex]

[tex]28 = a[/tex]

(OR)

[tex]a = 28.[/tex]


Related Questions

Please help!!
y= 1/2 x + 2
One equation in a system of two linear equations is
shown above. If the system has one solution (x, y),
where x = 2, which of the following could be the
other equation in the system?
A) y = -2x + 4
B) y = -x+ 5
C) y = 2x
D) y = 2x + 1

Answers

Answer:  B) y = -x+ 5

Step-by-step explanation:

If the x-value in the solution (x, y) is 2, then the y-value is:

[tex]y=\frac{1}{2} (2)+2 = \frac{2}{2} +2=1+2=3[/tex]

So the solution coordinate is (2, 3).

Test each of the answer choices to see if whether the y-value is 3 when the x-value is 2. If it's true, then it could be the other equation in the system.

A) y = -2x + 4

[tex]y = -2x + 4\\\y = -2(2) + 4 = -4 + 4 = 0[/tex]

B) y = -x+ 5

[tex]y = -x+ 5\\y = -(2) + 5 = 5 - 2 =3[/tex]

C) y = 2x

[tex]y=2x\\y=2(2)=4[/tex]

D) y = 2x + 1

[tex]y = 2x + 1\\y=2(2)+1=4+1=5[/tex]

i need help trying to solve this question to the nearest tenth of a degree

Answers

X = 25.1 degrees...........

suppose you start with a single bacterium of streptococcus at hour 0 , and it has a generation time of 60 minutes. how many bacteria will you have at the end of hour 24

Answers

Answer:

60x24

Step-by-step explanation:

60x24=1224

which graph best represents the line y= -1/5x+2

Answers

Answer:

B

Step-by-step explanation:

Line crosses y-axis at 2.

Slope = [tex]\frac{-1}{5}[/tex]

For each 1 square the line rises/falls it moves to the right/left 5 squares.

Negative slope lines are downhill left to right.  

The correct graph to represent the line y = -1/5 x + 2 will be;

⇒ Graph 2

What is Equation of line?

The equation of line with slope m and y intercept at point b is given as;

y = mx + b

Given that;

The equation of line is;

⇒ y = - 1/5 x + 2

Now,

The standard form of the equation of line with slope m and y intercept at point b is given as;

y = mx + b

By comparing we get;

Slope (m) = - 1/5

In the second figure;

Let two points on the graph (0, 2) and (5 , 1).

So, Slope is defined as;

m = (1 - 2) / (5 - 0)

m = - 1 / 5

And, Clearly the y - intercept is at point 2.

Therefore,

Graph 2 shows the correct graph to represent the line y = -1/5 x + 2.

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Mr. Lord borrowed $100,000 from a bank at a rate of 8% per annum for 3 years. Calculate the amount accruing for the loan

Answers

Answer: [tex]\$125,971.2[/tex]

Step-by-step explanation:

Given

Principal amount [tex]P=\$100,000[/tex]

Rate of interest [tex]r=8\%[/tex]

Time period [tex]t=3\ yr[/tex]

Amount in compound interest is given by

[tex]\Rightarrow A=P\left(1+r\%\right)^t\\\Rightarrow A=100,000(1+0.08)^3\\\Rightarrow A=\$125,971.2[/tex]

Thus, the amount accruing for loan is [tex]\$125,971.2[/tex]

What is the measure of angle ABC of a circle

Answers

Answer:

the angle <ABC is equal to 65°

Someone please help me ASAP!

Answers

Answer:

y axis then translate x+1,y+1

Which is the graph of the linear inequality x - 2y > -6?
-10-
2
108
0
o

Answers

Answer:

the fourth option

Step-by-step explanation:

1/2x - 2y > -6

1/2x + 6 > y

or

y < 1/2x + 6

so, the solution is all the y values smaller (= below) the line function.

and because it is "<" and not "<=" the line itself is not included

can anyone help with integers?

Fill in the blanks.

6) 83 + 17 = 17 +

7) |46| – |50| =

8) 42 – 2 + (18 – 10) =

9) 18 – (3 – 1) =

10) 8 - 0 =

Answers

Answer:

a) 83,b) -4,c) 48,d) 16,e) 8

plz help ASAP with explanation

Answers

These are the answers but seriously… It’s simple multiplication That’s the explanation

Answer:

(in image attached)

Step-by-step explanation:

A.

Left: 6×-3

Right: -3×-2

Bottom: 6×-2

B.

48÷6 = 8

-42÷6 = -7

-56÷8 = -7

-56÷-7= 8

given the figure below, what is the value of x?

Answers

Answer:

x = 6

Step-by-step explanation:

6 is x so this is the answer

Find the area of the region between the curve x^3+2x^2-3x and the x-axis over the interval [-3,1]

Answers

Answer:

[tex]\displaystyle A = \frac{32}{3}[/tex]

General Formulas and Concepts:

Calculus

Integrals

Definite IntegralsArea under the curve

Integration Rule [Reverse Power Rule]:                                                                   [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                        [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                             [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                           [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Area of a Region Formula:                                                                                       [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

Curve: x³ + 2x² - 3x

Interval: [-3, 1]

Step 2: Find Area

Set up:                                                                                                               [tex]\displaystyle A = \int\limits^1_{-3} {(x^3 + 2x^2 - 3x)} \, dx[/tex][Integral] Rewrite [Integration Property - Addition/Subtraction]:                   [tex]\displaystyle A = \int\limits^1_{-3} {x^3} \, dx + \int\limits^1_{-3} {2x^2} \, dx - \int\limits^1_{-3} {3x} \, dx[/tex][Integrals] Rewrite [Integration Property - Multiplied Constant]:                   [tex]\displaystyle A = \int\limits^1_{-3} {x^3} \, dx + 2\int\limits^1_{-3} {x^2} \, dx - 3\int\limits^1_{-3} {x} \, dx[/tex][Integrals] Integrate [Integration Rule - Reverse Power Rule]:                      [tex]\displaystyle A = (\frac{x^4}{4}) \bigg| \limits^1_{-3} + 2(\frac{x^3}{3}) \bigg| \limits^1_{-3} - 3(\frac{x^2}{2}) \bigg| \limits^1_{-3}[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]:              [tex]\displaystyle A = -20 + 2(\frac{28}{3}) - 3(-4)[/tex]Evaluate:                                                                                                           [tex]\displaystyle A = \frac{32}{3}[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Find the rate of change for the function of change from x=-3 to x=1

Answers

Answer:

She's, "HOT"!

Step-by-step explanation:

Please help me I don’t understand I have been working on this question for 14 minutes!!!m

Answers

Answer:

<A = <B

=> 8x - 8 = 5x + 25

<=> 3x = 33

<=> x = 11

with x = 11 => mB = 5.11 + 25 = 55 + 25 = 80⁰

Answer:

x=11

B=80

Step-by-step explanation:

8x-8=5x+25

3x=33

x=11

B=5(11)+25

B=80

Twice a number minus 25 is less than 89. Translate it into an inequality and find the solution

Answers

Answer:

2x-25<89

x<57

Step-by-step explanation:

2x-25<89

2x<89+25

2x<114

Divide by 2...

x<57

Hope this helped! Please mark brainliest :)

the width of a newspaper is 13 3/4 inches. The left margin is 7/16 inch and the right margin is 1/2 inch. what is the width of the written page inside the margin?

Answers

Answer:

biggafigure a

mnn

Step-by-step explanation:

Find the area of the figure below

Answers

Answer:

35.2 cm²

Step-by-step explanation:

The area is:

A = 2(3.5*2) + 7*2 + 2(1.8*2) = 35.2 cm²

We can find the area,

→ 2(3.5 × 2)+ (7 × 2) + 2(1.8 × 2)

→ 14 + 14 + 7.2

→ 35.2 cm²

Thus, the area is 35.2 cm².

Find the value of x,rounded to the nearest tenth

Answers

Answer:

Step-by-step explanation:

The formula for this is

14(20) = 25x and

280 =25x so

x = 11.2

The perimeter of a square is 16 cm. Find the length of its diagonal.​

Answers

Answer:

perimeter of a square is l+l+l+l

16+16+16+16=64

Answer:

4√2 cm

Step-by-step explanation:

Perimeter of square = 4a = 16cm

a = 16 / 4

a = 4 cm

Length of each side = 4 cm

Diagonal^2 = side^2 + side^2

= 4^2 + 4^2

= 16 + 16

Diagonal^2 = 32

Diagonal = 4√2 cm

The length of a side of an equilateral triangle is 40 centimeters.
What is the length of the altitude of the triangle?

Answers

Answer:

34.64 cm

Step-by-step explanation:

sin 60 = [tex]\frac{x}{40}[/tex]

sin 60 (40) = x

34.64 = x

equilateral triangles have 60° angles.

sin Ф = [tex]\frac{opposite}{hypotenuse}[/tex]

hypotenuse is 40. All sides are 40.

x = opposite or height of triangle.

When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with
mass 7 kg, the acceleration of the object is 4 m/s?. If the same force acts upon another object whose mass is 2 kg, what is this object's acceleration?

Answers

Answer:

14 m/s²

Step-by-step explanation:

From the question

a ∝ F/m.............. Equation 1

Where a = aceleration, m = mass, F = force

make F the subject of the equation

F = ma............ equation 2

Given: m = 7 kg, a = 4 m/s²

Therefore,

F = 7(4)

F = 28 N

For another object whose mass is 2 kg,

Make a the subject of equation 2

a = F/m

a = 28/2

a = 14 m/s²

Consider the following equations and name the property of equality used to solve for the variable.
A. x + 3.75 = 7

B. –3b = 18

C. StartFraction m Over 5 EndFraction = negative 25

D. m – 4 = 9

Answers

Answer:

Subtraction property ; x = 3.25

Division property ; - 6

multiplication property ; - 125

Addition property ; 13

Step-by-step explanation:

A.)

x + 3.75 = 7

Using the subtraction property : subtract 3.75 from both sides

x + 3.75 - 3.75 = 7 - 3.75

x = 3.25

B. )

–3b = 18

According to the division property :

Divide both sides by - 3

-3b / - 3 = 18 / - 3

b = - 6

C.)

m/5 = - 25

Using the multiplication property :

m/5 * 5 = - 25 * 5

m = - 125

D.)

m – 4 = 9

Using the addition property :

Add 4 to both sides :

m - 4 + 4 = 9 + 4

m = 13

Answer:

A. Subtraction property ; x = 3.25

B. Division property ; - 6

C. multiplication property ; - 125

D. Addition property ; 13

Step-by-step explanation:

Which equation can be used to determine the reference angle

Answers

Answer:

2nd option

Step-by-step explanation:

[tex]\frac{7\pi }{12}[/tex] is an angle in the second quadrant

Thus to find the reference angle, subtract from π , that is

r = π - θ

Maria has 72 flowers and four vases she put the same number of flowers in each vase how many flowers are in one vase

Answers

The answer is 18. Divide 72 by four.

Determine the value of x.

8 2
8 3
4
8

Answers

Answer:

Step-by-step explanation:

What is the solution to the equation One-fourth x + 2 = negative StartFraction 5 Over 8 EndFraction x minus 5?

x = negative 8

x = negative 7
pls hurry
x = 7

x = 8

Answers

Answer:

c = 24

Step-by-step explanation:

Which method is used in elimination to find the solutions of a - b = 9 and a + b = 5? ​

Answers

The substitution method is used in elimination to find the solution to the equation.

What is the system of two equations?

A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.

The given equation in the problem is;

Equation P: a - b = 9

Equation Q: a+b=5

The value obtained from the equation P is;

a - b = 9

a=b+9

Substitute the value in the equation Q;

a+b=5

b+9+b=5

2b=9-5

b=2

The value of a is;

a-b=9

a-2=9

a=9+2

a=11

Hence the value of a and b will be 11 and 2.

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lic/activity/6000001/assessment
1 Pretest: Unit 6
Question 1 of 21
What is the domain of the exponential function shown below?
Rx) = 5.3x

Answers

Given:

The exponential function is:

[tex]R(x)=(5.3)^x[/tex]

To find:

The domain of the given exponential function.

Solution:

We know that the general form of an exponential function is:

[tex]f(x)=ab^x[/tex]

Where, a is the initial value and b is growth/decay factor.

This function is defined for all real values of x, so the domain of these type of functions is the set of all real number.

We have,

[tex]R(x)=(5.3)^x[/tex]

Here, a is 1 and b is 5.3. This function is defined for all real values of x

Therefore, the domain of these type of functions is the set of all real number or it can be written as [tex](-\infty,\infty)[/tex].

Given that the expression 2x^3 + mx^2 + nx + c leaves the same remainder when divided by x -2 or by x+1 I prove that m+n =-6

Answers

Given:

The expression is:

[tex]2x^3+mx^2+nx+c[/tex]

It leaves the same remainder when divided by x -2 or by x+1.

To prove:

[tex]m+n=-6[/tex]

Solution:

Remainder theorem: If a polynomial P(x) is divided by (x-c), thent he remainder is P(c).

Let the given polynomial is:

[tex]P(x)=2x^3+mx^2+nx+c[/tex]

It leaves the same remainder when divided by x -2 or by x+1. By using remainder theorem, we can say that

[tex]P(2)=P(-1)[/tex]              ...(i)

Substituting [tex]x=-1[/tex] in the given polynomial.

[tex]P(-1)=2(-1)^3+m(-1)^2+n(-1)+c[/tex]

[tex]P(-1)=-2+m-n+c[/tex]

Substituting [tex]x=2[/tex] in the given polynomial.

[tex]P(2)=2(2)^3+m(2)^2+n(2)+c[/tex]

[tex]P(2)=2(8)+m(4)+2n+c[/tex]

[tex]P(2)=16+4m+2n+c[/tex]

Now, substitute the values of P(2) and P(-1) in (i), we get

[tex]16+4m+2n+c=-2+m-n+c[/tex]

[tex]16+4m+2n+c+2-m+n-c=0[/tex]

[tex]18+3m+3n=0[/tex]

[tex]3m+3n=-18[/tex]

Divide both sides by 3.

[tex]\dfrac{3m+3n}{3}=\dfrac{-18}{3}[/tex]

[tex]m+n=-6[/tex]

Hence proved.

Solve the system of equations.

−5x−3y−9=0
4x−18y−54=0
y=? x=?

Answers

Answer:

Step-by-step explanation:

Eq. 1 )   −5x−3y−9=0

Eq. 2)   4x−18y−54=0

there are two routes to solve this,   Substitution or  elimination,  I'll go for the 2nd one because I can see that the y values are a multiple of each other :)

    6 *( −5x−3y−9=0 )

Eq. 3) -30x -18y =54

subtract Eq. 2 from Eq. 3  :)

-30x -18y =54

-( 4x−18y=54)

-34x = 0

so according to the equations then x =0 but,  that's not really a full answer, so now we should go back and try the other method, substitution,

then:

-5x = 9 +3y

x = - 9/5 + (-3/5)y

now plug that into Eq. 2

4( - 9/5 + (-3/5)y ) - 18y = 54

-36/5 + (-12/5)y -18y = 54

(-12/5)y - (90/5)y = 54+36/5

-(102/5)*y =270/5+36/5

-(102/5)y = 306/5

y = (-5/102)*(306/5)

y = -306/102

y = -3

then plug in for either equation

-5x-3( -3) = 9

-5x + 9 = 9

-5x = 0

x = 0

now we have the full answer

check it by plugging in both x and y into the 2nd equation

4(0) - 18(-3) = 54

54= 54

this seems good  

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