Divide using synthetic division, and write a summary statement in fraction form. 2x5-x4+3x2-x+5/x-1

Dan will earn £59.40 for 6 hours of work.

To calculate Dan's earnings for 6 hours of work, we can multiply his hourly rate (£9.90) by the number of hours (6).

So, Dan will earn £9.90 x 6 = £59.40 for 6 hours of work.

Therefore, Dan will earn £59.40 for 6 hours of work.

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Answer:

x = 1; y = 1; z = 0

Step-by-step explanation:

First problem:

First equation minus second equation: 3y + 2z = 3      Eq. A

Second equation plus third equation: 2y + 4z = 2        Eq. B

-2 times Eq. A plus Eq. B: -4y = -4

y = 1

Substitute y = 1 in Eq. A: 3 + 2z = 3

2z = 0

z = 0

Substitute z = 0 and y = 1 in original first equation:

-2x + 2 + 0 = 0

-2x = -2

x = 1

Answer: x = 1; y = 1; z = 0

ANSWER

The set of the intersection  of {[tex]2,3,5,7[/tex]} and {[tex]2,5,11,13[/tex]} is

{[tex]2,5[/tex]}

EXPLANATION

Let [tex]A=[/tex]{[tex]2,3,5,7[/tex]}

and

[tex]B=[/tex]{[tex]2,5,11,13[/tex]}.

The intersection of the two sets are the elements that are in both set A and set B.

The elements that are common to both sets are 2 and 5. So, we write;

[tex]A \cap B=[/tex]{[tex]2,5[/tex]}

Therefore the correct answer is C

The intersection of the sets {2,3,5,7} and {2,5,11,13} is the set {2,5}, which has the elements common to both sets. Therefore option c is correct

The intersection of two sets is the set of elements common to both sets. In the provided sets {2,3,5,7} and {2,5,11,13}, the common elements are 2 and 5. Therefore, the intersection of these two sets is {2,5}. So, the correct answer is C. {2,5}.

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Answer:

9

Step-by-step explanation:

0.9 per cent of 1000 = 0.9(1000)/100 = 0.9(10) =9

Answer: 4

Step-by-step explanation:

Find all of the factor pairs of 120, then look for the ones that are even-odd

         120

           ∧

      120   1     even-odd

        60   2    even-even

        40   3    even-odd

         30   4    even-even

         24   5    even-odd

         20   6    even-even

          8    15    even-odd

           10  12    even-even

There are 4 even-odd factors pairs for 120.

you said times and sum, sum is addition and times is multiplication so im confused. can you copy the exact question so i can help?

I believe it is A.  I did this awhile ago.

The standard form of the number 5.871x10⁻⁷ is 0.0000005871 after using the properties of the integer exponent.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The number is:

= 5.871x10⁻⁷

After using the properties of the integer exponent:

= 5.871x(1/10⁷)

= 5.871x(1/10000000)

= 5.871x0.0000001

= 0.0000005871

Thus, the standard form of the number 5.871x10⁻⁷ is 0.0000005871 after using the properties of the integer exponent.

Learn more about the integer exponent here:

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dude its b thats easy and yes im sure 4 units down and sense its not reflection then thats the answer

Hello!

Solve for y.

[tex]2x +4y =12[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓↓↓↓↓

First you had to add by -2x from both sides of the equation.

[tex]2x+4y+-2x=12+-2x[/tex]

[tex]4y=-2x+12[/tex]

Then divide by 4 from both sides of the equation.

[tex]\frac{4y}{4}=\frac{-2x+12}{4}[/tex]

Simplify it should be the correct answer.

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

Answer⇒⇒⇒⇒⇒⇒y=-1/2x+3

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

5/8 is the answer. I just x the numerator and denominator by 2 to be 6/8-1/8=5/8

The answer to this question is A

10 units up means to add 10 to the y-coordinate of the vertex (h, k).

p(x) = 0.005(x - 40)² + 60

p(x) shifted up 10 units = 0.005(x - 40)² + (60 + 10)

                                q(x) =  0.005(x - 40)² + 70  

In order to answer this question, you must do some multiplication!

So, in order to have a pair of shoes, you must have 2 shoes. There are 42 PAIRS of shoes. So if you wanna find the number of ALL of the shoes, you have to multiply da numbers.

42 × 2 = 84

There are 84 shoes altogether.

If you need anymore help, just let me know!

The number of shoes in one pair is two thus there will be 84 in the office.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.

Multiplication gives us a resultant number that will be very big compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

As per the given,

Number of pairs of shoes = 42

Number of shoes in one pair of shoes = 2

Total number of individual shoes = 42 x 2 = 84

Hence "The number of shoes in one pair is two thus there will be 84 in the office".

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ANSWER

Each side of the chip is 5 centimeters long.

EXPLANATION

The chip is in the form of a square.

The formula for finding the area of a square is

[tex]Area=l^2[/tex]

We were given in the question that, the area is 25 square centimeters. This means that,

[tex]25=l^2[/tex]

We take the square root of both sides to get,

[tex]\sqrt{25}=l[/tex]

[tex]\Rightarrow 5=l[/tex]

Hence the length of the square technology chip is 5 centimeters

The perimeter of △ABC is approximately 25.93 units. The area of △ABC is approximately 28.62 square units.

Given that △ABC has m∠A=60°, m∠C=45°, and AB=9, we can use trigonometry to find the missing side lengths and then use them to calculate the perimeter and area of the triangle.

First, we can use the fact that the sum of the angles in a triangle is 180° to find m∠B:

m∠A + m∠B + m∠C = 180°

60° + m∠B + 45° = 180°

m∠B = 75°

Next, we can use the law of sines to find the length of side BC:

sin 60° / 9 = sin 75° / BC

BC = sin 75° * 9 / sin 60°

BC ≈ 8.14

Finally, we can use the fact that the sum of the side lengths of a triangle is its perimeter to find the perimeter of △ABC:

Perimeter = AB + BC + AC

Perimeter = 9 + 8.14 + AC

To find AC, we can use the fact that the angles in a triangle add up to 180°:

m∠A + m∠B + m∠C = 180°

60° + 75° + m∠C = 180°

m∠C = 45°

Now we can use the law of sines again to find AC:

sin 45° / AC = sin 60° / 9

AC = sin 45° * 9 / sin 60°

AC ≈ 7.79

Substituting this value into the equation for the perimeter, we get:

Perimeter = 9 + 8.14 + 7.79

Perimeter ≈ 25.93

Therefore, the perimeter of △ABC is approximately 25.93 units.

To find the area of △ABC, we can use the formula for the area of a triangle:

Area = 1/2 * base * height

We can use the fact that △ABC is a right triangle (since m∠C = 45°) to find the height:

sin 45° = height / 9

height = sin 45° * 9

height ≈ 6.36

Substituting the values for the base and height into the formula for the area, we get:

Area = 1/2 * 9 * 6.36

Area ≈ 28.62

Therefore, the area of △ABC is approximately 28.62 square units.

Perimeter of △ABC: 20.67 units,

Area of △ABC: 20.11 square units.

In △ABC, we are given that ∠A = 60°, ∠C = 45°, and AB = 9 units. To find the perimeter, we need to calculate the length of side BC. Using the angles, we can determine that ∠B = 180° - ∠A - ∠C = 75°. Now, applying the Law of Sines, we find BC ≈ 8.21 units. The perimeter, therefore, is the sum of the three sides: 9 + 8.21 + BC ≈ 20.67 units.

For the area, we can use the formula A = 0.5 * AB * BC * sin(∠C). Substituting the known values, we get A ≈ 0.5 * 9 * 8.21 * sin(45°) ≈ 20.11 square units.

Explanation:

In the main answer, we first addressed the perimeter by finding the length of side BC through the Law of Sines. The perimeter is then calculated by summing the three sides.

Moving on to the area, we employed the formula for the area of a triangle involving two sides and the sine of the included angle. Substituting the given values, we obtained the area of △ABC as approximately 20.11 square units.

These calculations showcase the application of trigonometric principles in solving geometric problems involving angles and side lengths. The Law of Sines and the area formula for triangles provide a mathematical framework for determining these essential properties.

answer is equal to 168/144

7/6feet

Answer:

45mins ÷ 15pages = 3

so she reads 3pages per minute

3pages × 60minutes = 180

she read 180pages in 60minutes

hope this helps

Step-by-step explanation:

Follow this as an example

An empty swimming pool needs to be filled to the top. The pool is shaped like a cylinder with a diameter of

10 m

and a depth of

1.4 m

. Suppose water is pumped into the pool at a rate of

11 m3

per hour. How many hours will it take to fill the empty pool?

Use the value

3.14

for

π

, and round your answer to the nearest hour. Do not round any intermediate computations.

The formula for the volume of a cylinder is  ∏r2h.  The problem gives d=10m, so r=5m.

The pool holds  (3.14)*52*1.4 m3 = 109.9 m3 of water.

At a rate of 11 m3 per hour:

            ( 109.9 m3 ) / (11 m3/hr)  = 9.990909 hr.

              rounding to the nearest hour, this is 10 hours

The pool has a volume of approximately 47.97 cubic meters. The pump can fill 11 cubic meters per hour. Therefore, rounding up, it will take roughly 5 hours to fill the pool.

The volume of the swimming pool shaped like a cylinder can be calculated using the formula for the volume of a cylinder which is V = πr2h, where r is the radius, h is the height (or depth in this case) and π is a constant whose value we'll take as 3.14. Therefore, the volume of the pool is V = 3.14 * (6/2)2 * 1.7.

Once we have the volume, we can divide this by the rate of water being pumped in, in terms of how many cubic meters it pumps per hour, to find out how many hours it would take. So the time taken to fill the pool, in hours, is Time = Volume / Rate.

By substituting the numbers we have into these formulas, we get V = 3.14 * 9 * 1.7 = 47.97 m3, and Time = 47.97 m3 / 11 m3/hour = approximately 4.36 hours. Since we need to round up to the nearest hour, the pool will take about 5 hours to fill.

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Let x represent the number of ounces of vinegar

Let y represent the number of ounces of lemon juice

Oil required = 8 oz

Container can hold = 16 oz

So the inequality equation will be :

[tex]x+y+8\leq16[/tex]

10 units

calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (- 5, 8 )

d = √(- 5 - 3 )² + (8 - 2 )²

  = √(64 + 36 ) = √100 = 10

Intercept form is: y = a(x - p)(x - q)  

It is given that:  p = 14, q = -6, x = 14, y = 4

4 = a(14 - 12)(14 - (-6))

4 = a(2)(20)

4 = 40a

[tex]\frac{4}{40} = \frac{40a}{40}[/tex]

[tex]\frac{1}{10} = a[/tex]

Answer: y = [tex]\frac{1}{10}[/tex](x - 14)(x + 6)

[tex]P(x)=(x+a)^5 + (x+c)^5 + (a-c)^5[/tex]

If [tex]x+a[/tex] is a factor of [tex]P(x)[/tex], then [tex]-a[/tex] is a root of [tex]P(x)[/tex].

Therefore

[tex](-a+a)^5+(-a+c)^5+(a-c)^5=0\\\\0^5+(-1(a-c))^5+(a-c)^5=0\\\\(-1)^5(a-c)^5+(a-c)^5=0\\\\-(a-c)^5+(a-c)^5=0\\\\0=0[/tex]

This is a more difficult one to explain. Let's start with the line to the right.  It has a slope (m) of [tex]\frac{-2}{2}[/tex] = -1 and a y-intercept of +3 (continue the line to see where it crosses the y-axis). So, the equation of that line is: y = -x + 3 when x ≥ 2. This can also be written as y = 3 - x when x ≥ 2.  The only option that has that equation is A.

Answer: A

First of all, you can see that this is a piecewise polynomial, since it is shaped like a parabola before [tex] x = 2 [/tex], and is a line after [tex] x = 2 [/tex] So, option C is surely wrong, because it uses [tex] x = 3 [/tex] as splitting point.

Moreover, the way the parabola "bounces" on the x axis, avoiding its negative part, tells us that there is an absolute value. This excludes options B and D, and the answer is thus A.

Answer:

Anything that does not cost more than $2,560.00

Step-by-step explanation:

Provided that Nikita is spending money that she had invested and the amount  she collected over the period of 7 years. She can buy any item that costs no more than $2,560.00 but how?

It is a problem of simple interest:

Here the principal amount (P) = $2,000.00

Interest rate (r) = 4%

Time period (t) = 7 years

So, total amount that she would get by the end of 7 years is:

[tex]A=P+SI[/tex]

[tex]SI=\frac{P\times r\times t}{100}[/tex]

Plugging the values we get:

[tex]SI=\frac{2000\times 4\times 7}{100}=560.00[/tex]

So the interest collected over 7 years is $560.00

Therefore, the total amount after 7 years is:

[tex]\$2000.00+\$560.00=\$2,560.00[/tex]

If Nikita is using this money then the most expensive item that she could buy will cost no more than $2,560.00.

Answer:

The answer is B (a mountain bike priced at $2,500) in Plato

Step-by-step explanation: