Divide using either synthetic division or long division.
(6x³ +5x² − 3x + 8) ÷ (x − 2)
-
a) 6x² - 7x² - 17x –
26
x-2
b) 6x² + 17x +31 +70
c) 6x³ + 17x² +31x + 70
d) 6x² + 17x +31 +
70
x-2

Yannick paid $9.25 as sales tax on the bicycle.

Here, we are given that Yannick bought a bicycle and paid $194.25 for it, including tax.

Let the cost of the bicycle without tax be x

We are given that the rate of sales tax is 5%

Thus, the amount of tax on bicycle will be-

5% of x

= (5/100)*x

= 0.05x

Thus, we can form an equation as follows-

x + 0.05x = 194.25

1.05x = 194.25

x = 194.25/ 1.05

x = 185

Thus, the cost of bicycle without tax is 185

Therefore, the tax paid will be-

0.05x

= 0.05*185

= 9.25

Thus, Yannick paid $9.25 as sales tax on the bicycle.

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Answer:

y = mx + b

y = 3/2x - 2

m = 3/2

b = -2

[tex]1 - 3 < x < 4 - 3 \\ - 2 < x < 1[/tex]

WHAT YOU DO ON OTHER SIDE OF THE INEQUALITY YOU HAVE TO DO IT ON EVERY SIDE TO BALANCE THE INEQUALITY

GOODLUCK.

Step-by-step explanation:

Brett bought three pairs of jeans and five polo shirts. The jeans that regularly sell for $79 were 35% off and the polo shirts that regularly sell for $39 were 15% off. If sales tax is 5.75% and he gave the cashier $350, how much did he receive back in change?​

3 pairs jeans at regular price costs: 79 * 3 = 237

35% off so paying 65% of full price:

237 * 0.65 = discounted price of 154.05

5 polo shirts at regular price costs: 39 * 5 = 195

15% off so paying 85% of full price:

195 * 0.85 = discounted price of 165.75

cost of jeans and polo shirts at discounted prices: 154.05 + 165.75 = 319.8

Pay an additional 5.75% sales tax. So Brett is paying 1.0575 of the cost:

1.0575 * 319.8 = 338.1885. Rounded, it cost Brett $338.19 for his jeans and polo shirts.

Brett gave $350:

350 - 338.19 = $11.81 change received

The solution of the inequality in the variable x <0.

Any monotonically rising function can, by definition, be applied to both sides of an inequality without violating the asymmetry connection (provided that both expressions are in the domain of that function). The inequality relation is flipped when a monotonically decreasing function is applied to both sides of an inequality. In the criteria for the basic inverse and the multiplicative inverse for positive values, a monotonically decaying function is utilized.

The given inequality is

4x + 2 <2

subtracting 2 from both sides

4x+2-2<2-2

or,4x < 0

or, x < 0

If the inequality is strict (a< b, a > b) and the function is strictly monotonic, the inequality remains strict. If only one of the preceding conditions is met, the ensuing imbalance does not exist. Indeed, the rules for addition and multiplicative exponentiation use a monotonically decreasing function.

Hence the solution of the inequality in the variable x <0.

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We have the following:

we calculate the new values

now, we calculate the mean

the standard deviation of the data set is:

The answer is the option C. 47.9

Answer:

[tex]f(x) = {x}^{4} - 16[/tex]

Step-by-step explanation:

[tex]f(x) = (x + 2i)(x - 2i)(x - 2)(x + 2)[/tex]

[tex]f(x) = ( {x}^{2} + 4)( {x}^{2} - 4) [/tex]

[tex]f(x) = {x}^{4} - 16[/tex]

The height of the tree in 30 months given the linear equation is 16m.

The given equation is a linear equation. A linear equation is an equation that changes at a constant rate. The change can either be an increase or a decrease. A linear equation usually has an intercept and a slope. The intercept is the value of the equation when x is zero. The slope is the rate of change of the equation.

H (x) = 10 + 0.20x

10 = intercept

0.20 = slope

In order to determine the height of the tree after 30 months, substitute for x in the above linear equation.

H(x) = 10 + (0.2 x 30)

H(x) = 10 + 6

H(x) = 16

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Answer:

60 Sq in

Step-by-step explanation:

14×6= 84

4×6=24

84-24= 60

The equation of line in point-slope form is; 7y = x + 31.

For the given question;

The points are given as;

(x₁, y₁) = (4, 5)

(x₂, y₂) = (-3, 4)

The slope of the equation of the line is found as;

slope = m = (y₂ - y₁)/(x₂ - x₁)

Put the values;

m = (4 - 5)/(-3 - 4)

m = (-1)/(-7)

m = 1/7

Thus, the point slope form will be;

y - y₁ = m(x - x₁)

y - 5 = (1/7)(x - 4)

Simplifying;

7y - 35 = x - 4

7y = x + 31

Thus, the equation of line in point slope form is; 7y = x + 31.

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Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

5√16² = 5(16^1/2)

Answer:

< 3 = 90°, < 8 = 43° and < 4 = 146°

Step-by-step explanation:

Since < 1 and < 3 are on the same straight line, < 3 = 180° - 90°.

Since < 6 = 137° and < 6 and < 8 are on the same straight line, < 8 = 180° - 137° = 43°.

Since < 2 = 34° and < 2 and < 4 are on the same straight line, < 4 = 180° - 34° = 146°.

Based on the cost to service the lawn, and the area of the lawn, the total cost of lawn service is $55.65

The first thing to do is to find the area of the lawn:

= Length of lawn x Width of lawn

= 40 x 190

= 7,600 square feet

The cost of each lawn is $42.00 of the first 5,000 square feet and then there will be $5.25 paid for each additional square feet.

The total cost of the lawn service is:

= 42.00 + ( 5.25 x (7,600 - 5,000) / 1,000)

= 42.00 + (5.25 x 2.6)

= $55.65

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Answer:

Step-by-step explanation:

x = 19 is the value of x in triangle .

What is triangle explain?

angle R + angle S + angle T = 180

(5+ 2x) + (7x - 16) + (x + 1) = 180

10x - 10 = 180

10x = 190

x = 19

Therefore

angle R = 5 + 2(19) = 43 degrees

angle S = 19 + 1 = 20 degrees

angle T = 7(19)-16 = 117 degrees

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In the given figure,

line a is parallel to line b,

Therefore,

∠1 + ∠90° = 180° ............... (Since they are Linear pairs)

⇒ ∠1 = 90°

∠1 = ∠3 and ∠2 = ∠90°............. (Vertically opposite angles)

⇒ ∠1 = ∠3 = ∠2 = ∠90°

∠2 = ∠4 and ∠3 = ∠5 ................ (Alternate interior angles)

⇒ ∠4 = ∠5 = ∠90°

∠4 = ∠6 and ∠5 = ∠7 ............. (Vertically opposite angles)

⇒ ∠6 = ∠7 = ∠90°

So,

∠1 = ∠2 = ∠3 = ∠4 = ∠5 =∠6 = ∠7 = 90°

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Base of the Prism = 5 cm

Height of the Prism = 4 cm

Length of the Prism = 6 cm

The volume of a triangular prism = 1/2 x base x height x length

⇒ Volume = 1/2 x 5 x 4 x 6

⇒ Volume = 60 cm^3

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The required transformation of the regular polygon to onto itself is a rotation by the angle of 360° around its own center or any point in the plane.

Given that,
To determine which transformation carries the given regular polygon onto itself.

Here,
According to the question as asked.
There are only 2 usual possible ways of transforming a regular polygon that will onto itself as,
(1) A perfect rotation of 360° around its own center.
(2) A rotation of 360° around any point in the space and plane containing the regular polygon.

Thus, the required transformation of the regular polygon to onto itself is a rotation by the angle of 360° around its own center or any point in the plane.

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Function B equation is

The y-intercept is when x=0, in our case

Function A

y-intercept =3

Function B

y-intercept=-5

As we can see

The y-intercept of Function A is greater than the y-intercept of Function B.

Brock is at a distance of 621/40 miles away from home.

Here, we are given that Brock rides his bike 22 1/8 miles to the nature preserve.

This means that he is now 22 1/8 miles away from his home. Now, he starts on his way home and after 16 1/5 miles, he stops at a deli for lunch.

Thus, he is now 22 1/8 - 16 1/5 miles away from his home.

To subtract the fractions we need to convert the mixed fractions into improper fractions, which can be done as follows-

22 1/8 = (22*8 + 1)/8

= 177/8

and 16 1/5 = (16*5 + 1)/5

= 33/5

Thus, the expression becomes-

177/8 - 33/5

now, we need to make the denominators of each fraction so that we can subtract them.

= (177*5)/40 - (33*8)/40

= 885/40 - 264/40

= 621/40

Thus, Brock is at a distance of 621/40 miles away from home.

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The information that is not needed to determine the total bill after tax is is the tax was 7%.

The total bill is $11.

The total bill paid is the sum of the cost of the meal, tax and the tip paid. The tip and tax would increase in the total amount that is paid by the customers.

Tax is a compulsory amount that is levied by the government on certain goods and services.

Percentage is the fraction of an amount expressed as a number out of hundred. To convert a number from percentage to a number, divide the percentage by 100.

Tax paid = 10% x total bill

$1.10 = 0.1 x b

1.10 = 0.1b

b = 1.10 / 0.1

b = $11

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a. The information that is needed to solve the problem is D. All of this information is needed to solve the problem.

b. The total bill is $117.

It should be noted that an expression shows the relationship between the numbers or the variables

The total bill will be:

Tip = $1.10

Tax = 7%

Tip = 10% of cost:

$10 = 10% × c

0.1c = $10

c = $10/0.1 = $100

Cost = $100

The total bill. = Cost + Tip + Tax

= $100 + $10 + (7% × $100)

= $100 + $10 + $7

= $117

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Answer:

104 swimmers

Step-by-step explanation:

ratio is 8:1

8 : 1

x : 13

x = 8 multiplied by 13

swimmers = 104

Answer:

x = 7

Step-by-step explanation:

since 2 sides are congruent, then the triangle is isosceles with base angles being congruent , both (9x - 25)

the sum of the 3 angles in the triangle = 180° , that is

9x - 25 + 9x - 25 + 104 = 180

18x + 54 = 180 ( subtract 54 from both sides )

18x = 126 ( divide both sides by 18 )

x = 7

Answer:

the percentage is 100g divided by 5 to get 20

Answer:

Step-by-step explanation: a rate per 100 g packet