Which statement is true

Answer:

3. aₙ = -9n +7

4. d = -2.4

5. a₆ = 45

6. aₙ = 133 + 4n

Step-by-step explanation:

Question 3.

a₁ = -2; aₙ = aₙ₋₁ - 9

The explicit rule for an arithmetic sequence is

        aₙ = a₁ + d(n -1 )

         d = aₙ - aₙ₋₁

        aₙ = aₙ₋₁ - 9     Subtract aₙ₋₁ from each side

aₙ - aₙ₋₁ = -9

         d = -9

For this sequence,  

aₙ = -2 – 9(n - 1)     Remove parentheses

aₙ = -2 - 9n + 9      Combine like terms

aₙ = -9n + 7

===============

Question 4

d = aₙ - aₙ₋₁

a₂ - a₁ = 6.2 – 8.6 = -2.4

a₃ - a₂ = 3.8 – 6.2 = -2.4, etc.

The common difference is

d = -2.4

===============

Question 5

aₙ = 8n – 3     Substitute the value of n

a₆ = 8×6 – 3

a₆ = 48 - 3

a₆ = 45

============

Question 6

a₁ = 137; d = 4

aₙ = a₁ + d(n -1 )

aₙ = 137 + 4(n -1 )

aₙ = 137 + 4n -4

aₙ = 133 + 4n

Answer:

Slope (m) = 0.2 and y-intercept (b) = 3.5.

Step-by-step explanation:

We are given weather equation y=0.2x +3.5 for finding the amount of accumulated snow y in inches x hours after 5 P.M. on a certain day.

We need to identify the slope and y- intercept of the graph of the equation .

Let us compare given equation y=0.2x +3.5 by slope-intercept form y=mx+b, we get

Slope (m) = 0.2 and y-intercept (b) = 3.5.

Answer:

(x, y) = (- 3, 3)

Step-by-step explanation:

given the 2 equations

- x + 3y = 12 → (1)

y = 6x + 21 → (2)

Substitute y = 6x + 21 into (1)

- x + 3(6x + 21) = 12 ← distribute

- x + 18x + 63 = 12

17x + 63 = 12 ( subtract 63 from both sides )

17x = - 51 ( divide both sides by 17 )

x = - 3

Substitute  x = - 3 into (2) for y

y = (6 × - 3 ) + 21 = - 18 + 21 = 3

solution is (- 3, 3 )

Answer:

x = 4 1/2 or 4.5 cm

Step-by-step explanation:

We know the perimeter of the rectangle is given by the formula

P =2(l+w)

19 = 2(2.5 + (2.5+x))

Simplifying

19 = 2( 5+x)

Distribute

19 = 10 + 2x

Subtract 10 from each side

19-10 = 10-10 + 2x

9 = 2x

Divide each side by 2

9/2 = 2x/2

4.5 = x

f(2) This means that x is 2, so you can plug in 2 for "x" in the equation

f(x) = 3x - 12

f(2) = 3(2) - 12

f(2) = 6 - 12

f(2) = -6

Your answer is D

Answer:

D. -6

Step-by-step explanation:

Hi!!! You have to substitute 2 for f(x) & for the x next to 3!!!

f(x) = 3x- 12

f(2) = 3(2) - 12

= 6 - 12

= 6 -12

= -6

Answer: [tex]w=-\frac{1}{5}[/tex]

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have the following equation given in the problem above:

[tex]5 -5w= 6[/tex]

2. Then, you need to solve for [tex]w[/tex], as you can see in the following steps:

[tex]5-5w=6\\-5w=6-5\\-5w=1\\w=-\frac{1}{5}[/tex]

3. Therefore, as you can see, the value of [tex]w[/tex] is:

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

[tex]a-the\ side\ of\ square\\a^2-the\ area\ of\ square\\\\a+3-the\ one\ side\ of\ rectangle\\a-2-the\ second\ side\ of\ rectangle\\(a+3)(a-2)-the\ area\ of\ rectangle\\\\\text{The equation:}\\\\(a+3)(a-2)=a^2+30\qquad\text{use distributive property}\\\\(a)(a)+(a)(-2)+(3)(a)+(3)(-2)=a^2+30\\\\a^2-2a+3a-6=a^2+30\qquad\text{subtract}\ a^2\ \text{from both sides}\\\\a-6=30\qquad\text{add 6 to both sides}\\\\\boxed{a=36}\\\\Answer:\ \boxed{36\ cm}[/tex]

Answer:

first, you add the hours driven then you divide.

2+1.4+1.25=4.65

336/4.65=72.3

Step-by-step explanation:

Answer:the answer would be a i just did it but correct me if i was wrong

Step-by-step explanation:

Answer:

b. $3,000.00

Step-by-step explanation:

Daniel buys one bond each with a par value of $1,000 from Grath Oil, Ombor Medical Supplies, and Dwyn Horticulture.

Grath Oil bonds are selling at 120.514

Ombor Medical Supplies bonds are selling at 90.773

Dwyn Horticulture bonds are selling at 101.180.

These values have nothing to do here as we only have to find the face value.

The face value of 1 bond is $1000 so, the face value of 3 bonds will be = [tex]1000\times3=3000[/tex] dollars.

Answer:

The answer is (r + 3)(r - 3)

Step-by-step explanation:

There need to be two number that add together to get 0

and two number that multiply together to get -9

3 + -3 = 0

3 · -3 = -9

= (r + 3)(r - 3)

The graph described by the student shows a solid vertical line through the point (5, 0), with shading to the left. This corresponds to the inequality 'x less than or equal to 5'.

The student is asking about a graph of an inequality which features a solid vertical line that passes through the point (5, 0). The graph has shading to the left of this line. A vertical line in coordinate geometry represents all points where the x-coordinate is a specific value, and if the shading is to the left, it indicates that the x-values are less than or equal to that specific value of the vertical line.

Therefore, the correct inequality that matches the described graph is x less than or equal to 5 (`x ≤ 5`). The other options do not correctly represent a vertical line or the indicated shading direction.

Answer:

associative property of multiplication

Step-by-step explanation:

Associative property of multiplication states that (a x b) x c = a x (b x c).

5 * (sqrt(9) *4) = (5* sqrt(9) ) *4

Answer:B

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (7, -1) and (9, -9). Substitute:

[tex]d=\sqrt{(9-7)^2+(-9-(-1))^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}\\\\=\qrt{4\cdot17}=\sqrt4\cdot\sqrt{17}=\boxed{2\sqrt{17}}[/tex]

The distance between the points (7, -1) and (9, -9) is calculated using the distance formula and simplifies to [tex]2\sqrt{17}[/tex] units.

To find the distance between two points in simplest radical form, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]. For the points (7, -1) and (9, -9), the calculation is as follows:

First, find the difference in the x-coordinates: 9 - 7 = 2.

Next, find the difference in the y-coordinates: -9 - (-1) = -8.

Now, square each difference: (2)^2 = 4 and (-8)^2 = 64.

Add these squares together: 4 + 64 = 68.

Finally, take the square root of the sum: [tex]\sqrt{68}[/tex].

This radical simplifies to [tex]\sqrt{4 * 17} = 2\sqrt{17}[/tex], which is in simplest radical form.

Therefore, the distance between the points (7, -1) and (9, -9) is [tex]2\sqrt{17}[/tex] units.

Answer:

x= 60.1 degrees

Step-by-step explanation:

The triangle forms a right angle triangle

Opposite side of angle x = 13 ft

Hypotenuse of the triangle = 15

We know the opposite side and the hypotenuse

So we use trigonometric formula sin(x)

[tex]sin(x) = \frac{opposite}{hypotenuse}[/tex]

[tex]sin(x) = \frac{13}{15}[/tex]

When we move 'sin' to the other side it becomes 'sin^-1'

[tex]x=sin^{-1}(\frac{13}{15})[/tex]

x = 60.073565

Answer:x = 60.073565

Step-by-step explanation:

Answer:

Tate has 7x pennies.

Step-by-step explanation:

Tate has 2x pennies because Mia has x pennies and Tate has twice the pennies of Mia so

5+2x= 7x

Final answer:

To solve 8(5x+9x+6)=160, we first combine like terms to simplify the expression within the parentheses to 14x+6, and then use the distributive property to further simplify and solve the equation. This order of operations ensures clarity and accuracy in solving the equation.

Explanation:

The question involves solving the algebraic expression 8(5x+9x+6)=160. The first step in simplifying and solving an equation like this is to combine like terms within the parentheses. Combining like terms (5x+9x) simplifies the expression inside the parentheses to 14x+6. This simplification makes the equation easier to manage and understand. The next step is to use the distributive property which allows us to multiply the number outside the parenthesis (in this case, 8) by each term inside the parenthesis individually (14x and 6). After distributing, we get 112x + 48 = 160, from which we can solve for x by isolating the variable.

The order of operations is crucial here; combining like terms before using the distributive property ensures the equation remains manageable and reduces the potential for errors. After these steps, we can subtract 48 from both sides and divide by 112 to find the value of x that satisfies the equation.

Answer:

35q-384 = 225q-189

Step-by-step explanation:

since its 384 subtracted from 35 times q it will be 35q-384 and then it says "is" which is an equal sign (=) and then q times 225 which is 225q decreased by 189 which is 225q-189 so it will be 35q-384 = 225q-189

[tex]1/4(20-4a)=6-a \ /\cdot4\\20-4a=24-4a\\-4a+4a=24-20\\0=4\\false[/tex]

Answer:

I would combine like terms

Step-by-step explanation:

2/3x + 1/3x + =5

The first step would be to combine like terms

2/3 x + 1/3 x  = x

Answer:

  9/10 hours

Step-by-step explanation:

You want the total of 1/2 hours and 2/5 hours.

Addition of fractions is accomplished by converting them to values that have a common denominator.

  1/2 = 5/10

  2/5 = 4/10

Then the sum is ...

  1/2 +2/5 = (5/10) +(4/10) = (5 +4)/10 = 9/10

Manuel spent 9/10 hours on the two assignments.

__

Additional comment

Equivalently, you can convert the fractions to decimals and add them that way:

  1/2 +2/5 = 0.5 +0.4 = 0.9 . . . . . 9/10 hours

Your calculator can tell you what the sum is.

Final answer:

After calculating the cost per ounce for both packages, the 10.5-ounce package, with a unit price of $0.284 per ounce, is the better deal compared to the 27.8-ounce package, which has a unit price of $0.323 per ounce.

Explanation:

To determine which package has the better unit price, you calculate the cost per ounce for each package and compare them. First, divide the total cost of each package by the number of ounces it contains.

For the 10.5-ounce package at $2.98:

$2.98 ÷ 10.5 ounces = approximately $0.284 per ounce

For the 27.8-ounce package at $8.99:

$8.99 ÷ 27.8 ounces = approximately $0.323 per ounce

Now, compare the unit prices. The 10.5-ounce package has a lower unit price of $0.284 per ounce compared to the 27.8-ounce package with a unit price of $0.323 per ounce, making the 10.5-ounce package the better deal based on unit price.

The green square is the larger square, the total area for the target would be 8 x 8 = 64 square units.

The area of the smaller yellow square would be 4 x 4 = 16 square units.

The green area would be the difference between the total target area and the yellow area: 64 - 16 = 48 square units.

The probability of hitting the green area = 48 / 64 = 0.75

The answer is C.

Answer:

$27.83

Step-by-step explanation:

26.50 x .05 = 1.325  (round up to 1.33 since the 5 is 5 or greater)  

26.50 + 1.33 = 27.83  

Amount of tax will be 1.33

Answer:

27.83

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

First, we need to isolate all the x's on one side. To do this we need to move the -20 over to the other side making it a +20:

3.5x + 1/2x = 40 + 20 - 2x

Add the x's and the 40 and 20:

4x = 60 - 2x

Move the -2x over to the other side making it a +2x:

4x + 2x = 60

6x = 60

Divide both sides by 6:

x = 10

So x = 10

Answer:

10

Step-by-step explanation:

3.5(x) + -20 + 1/2(x) = 40 - 2x

3.5x - 20 + x/2 = 40 - 2x

3.5x + x/2 + 2x = 40 + 20

6x = 60

x = 60/6

    = 10

Answer:

y= 2x-4   ,   y= -1/2x +3    , y= -2/3x+2

Step-by-step explanation:

slope intercept form: y=mx+b

y-2x=-4

add 2x to both sides

y= 2x-4

y-3= -1/2x

add 3 to both sides

y= -1/2x +3

2x+3y=6

subtract 2x from both sides

3y= -2x+6

divide both sides by 3

y= (-2x+6)/3

y= -2/3x+2

NOTES:

Slope-Intercept form is y = mx + b  ; where m is the slope and b is the y-intercept.

To convert an equation into slope-intercept form, solve for y

******************************************************************************************

Answer: y = 2x - 4

Step-by-step explanation:

y - 2x = -4

  +2x    +2x  

y       = 2x - 4

********************************************************************************************

Answer: y = [tex]-\frac{1}{2}x[/tex] + 3

Step-by-step explanation:

y - 3 = [tex]-\frac{1}{2}x[/tex]

  +3          +3  

y       = [tex]-\frac{1}{2}x[/tex] + 3

********************************************************************************************

Answer: y = [tex]-\frac{2}{3}x[/tex] + 2

Step-by-step explanation:

2x + 3y = 6

-2x         -2x  

        3y = -2x + 6

        ÷3    ÷3  ÷3  

          y = [tex]-\frac{2}{3}x[/tex] + 2

Answer:

[tex]\frac{1}{81}[/tex]

Step-by-step explanation:

Law of exponent

[tex]a^{-m} = \frac{1}{a^{m} }[/tex]

1) Applying the above rule, we have

[tex]9^{-2} = \frac{1}{9^{2} }[/tex]

= [tex]\frac{1}{9*9}[/tex]

= [tex]\frac{1}{81}[/tex]

Answer:

C. b^27

Step-by-step explanation:

By the definition of exponents

[tex](b^9)^3=b^9*b^9*b^9[/tex]

And since for any real numbers [tex]r,x,[/tex] and [tex]y[/tex]

[tex]r^x*r^y=r^{(x+y)}[/tex]

This makes

[tex](b^9)^3=b^9*b^9*b^9=b^{{9+9+9}}=\boxed{b^{27}}[/tex]

Which is choice C.

Alternatively, we could use the identity

[tex](r^x)^y=r^{xy}[/tex]

in which case

[tex](b^9)^3=b^{(9*3)}= \boxed{b^{27}}[/tex]

which is the same answer.

Answer:b²⁷

Step-by-step explanation: