If f(x) = 4x6 + x² + 4, then what is the remainder when f(x) is divided by x -1?​

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Explanation:

I'll use the substitution method to solve this system of equations.

Solve the third equation for z

2x+z = 5

z = 5-2x

Then solve the second equation for y

x+2y = 5

2y = 5-x

y = (5-x)/2

y = -0.5x+2.5

Plug each of these into the first equation so we can solve for x.

x+y+z = 6

x+(-0.5x+2.5)+(5-2x) = 6

-1.5x+7.5 = 6

-1.5x = 6-7.5

-1.5x = -1.5

x = (-1.5)/(-1.5)

x = 1

Let's use this to find y and z

y = -0.5x+2.5 = -0.5*1+2.5 = 2

z = 5-2x = 5-2*1 = 3

Therefore,

x = 1

y = 2

z = 3

Or we can write it like this:  (x,y,z) = (1,2,3)

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Check:

Plug these values into equation 1 and simplify

x+y+z = 6

1+2+3 = 6

6 = 6

We get the same thing on both sides.

This confirms equation 1.

Repeat for equation 2.

x+2y = 5

1+2*2 = 5

1+4 = 5

5 = 5

This confirms equation 2.

Lastly, plug those values into equation 3

2x+z = 5

2*1+3 = 5

2+3 = 5

5 = 5

Equation 3 is confirmed.

All three equations are true when (x,y,z) = (1,2,3). The solution is fully confirmed.

The other side of the fence based on the information illustrated is 6.5 feet.

It should be noted that the perimeter of a rectangle is illustrated as:

= 2(length + width)

In this case, the width is given as 7/2 = 3.5 feet.

It should be noted that the perimeter is given as 20 feet.

Therefore, the length will be:

2(length + width) = 30

2(length + 3.5) = 20

2Length + 7 = 20

2L = 20 - 7

2L = 13

L = 13/2

L = 6.5

Therefore, the length is 6.5 feet.

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The probability of rolling exactly  one six = 0.04

what is probability ?

Probability is a branch of mathematics that deals with the occurrence from of a random event . the value is expressed from zero to one .Probability has been introduced in mathematics  to predict how likely events are to happen .

So , acc the question "exactly one six " means  that one roll so that probability must be doubled the probability of " not six " is 4/5 . the probability of a 6 on the roll and not on the second is 1/5 x 4/5 =4/ 25 .

The six could come on the second roll so thst probability must be doubled .

the overall probability of exactly one six 8/25 or 0.32

completing toatl probability -no sixes =4/25 x 4/25 =16/25 =0.04

two sixes =1/5x 1/5 =1/25= 0.04

Hence , the probability of rolling exactly one six = 0.04

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The supergym sold 15,826.24 membership last year

This year it's employees sold 10,412

This number is 52% more that they sold last year

The first step is to calculate 52% of 10,412

52/100 × 10,412

= 0.52 × 10412

= 5,414.24

The number of membership sold this year can be calculated as follows

= 5414.24 + 10,412

= 15,826.24

Hence the number of membership they sold last year is  15,826.24

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Answer:

Five coins are tossed the probability of getting two heads is 5/16.

Step-by-step explanation:

I hope it will be helpful for you.

Answer:

Let C=the number of candies (because the first variable starts with c)

Let p= the number of pretzels (because the second variable starts with p)

SYSTEM OF EQUATIONS:

4.25c+3.50p=36.50 (first variable number + 2nd variable number equals total amount

p=c+6 (we know we have 6 more pretzels than candies to we have to add candies(c)+6 how many more pretzels than candy we have to find pretzels total number.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 216/3

Step-by-step explanation:

1 minute / 3 minutes = 1/3

216 feet * 1/3 = 216/3 feet per minute

Answer:

72 feet

Step-by-step explanation:

This question tests on the concept of conversion.

Given from the question, given the man can walk 216 feet in 3 minutes,

3 minutes = 216 feet

(3÷3) minute = (216 ÷ 3) feet

1 minute = 72 feet

Answer:

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

PEMDAS

multiplication and division are on the same level, when you see both work from left to right

addition and subtraction are also on the same leve, work from left to Right

P > E > M = D > A = S

Answer:

p e m d a s

Step-by-step explanation:

I hope it's helpful for you

The equation of the line that goes through the point (3,-3) and has a slope of -5/3 is y=(-5x+6)/3.

In mathematics, line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent a slope; reason for this is unclear, although it is first used in English by O'Brien in 1844, who wrote the equation for a straight line as "y = mx + b," and by Todhunter in 1888, who wrote it as "y = mx + c."

The ratio of "vertical change" to "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as quotient ("rise over run"), which produces same number for every two distinct points on the same line. A declining line has negative "rise." The line might be useful, as determined by road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.

The slope's absolute value serves as a gauge for  line's steepness, incline, or grade. A steeper line is indicated by slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical.

if we let y = mx + b, where m is the slope and b is the intercept, and y - y1 = m (x - x1), then:

3(y + 3) = - 5 (X - (-3))

3y + 9 = - 5 X + 15

3y = -5 X + 6

y=(-5x+6)/3

Check:

When x = 3, y should equal - 3, so:

Y = (- 5 (3) + 6)/3 = -3

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Answer:

Congruent shapes are shapes that are exactly the same. The corresponding sides are the same and the corresponding angles are the same.

Answer: Congruent mean same/equal

Step-by-step explanation: So if the have the same height,width, radius,or even angles, they can be congruent.

The dimensions of the rectangular prisms are:

Prism M: l=4 cm , w=1 cm and h=6 cm

Prism W: l=2 cm , w=2 cm and h=6 cm

Prism Z: l=6 cm , w=1 cm and h=4 cm

Prism J: l=2 cm , w=4 cm and h=3 cm

Prism R: l=2 cm , w=3 cm and h=4 cm

Prism F: l=1 cm , w=8 cm and h=3 cm

Given, a rectangular prism with a volume of 24 cm³

Dimensions of the prism if the volume is 24 cm³.

Prism M:

l=4 cm and w=1 cm

we know that volume = h×l×w

h×4×1=24

4h=24

h=24/4

h=6 cm

Prism W:

l=4 cm and w=2 cm

we know that volume = h×l×w

h×2×2=24

4h=24

h=24/4

h=6 cm

Prism Z:

l=4 cm and w=1 cm

we know that volume = h×l×w

h×6×1=24

6h=24

h=24/6

h=4 cm

Prism J:

l=2 cm and w=4 cm

we know that volume = h×l×w

h×2×4=24

8h=24

h=24/8

h=3 cm

Prism R:

l=2 cm and w=3 cm

we know that volume = h×l×w

h×2×3=24

6h=24

h=24/6

h=4 cm

Prism F:

l=1 cm and w=8 cm

we know that volume = h×l×w

h×1×8=24

8h=24

h=24/8

h=3 cm

hence we get the required dimensions.

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It should be noted that 10^-3 × 10^6 in scientific notation is 10³.

It should be noted that scientific notation is simply used in Mathematics to express the numbers that are either too small or too large.

This will be illustrated based on the information given. In this case, we want to multiply 10^-3 × 10^6. This will be illustrated thus:

= 10^-3 × 10^6.

It should be noted that since the question is about multiplication, the powers will be added.

= 10^-3 × 10^6.

= 10³

The answer is 10³.

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Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=8\\ b=12\\ h=7 \end{cases}\implies A=\cfrac{7(8+12)}{2}\implies A=70[/tex]

Answer:

2/3

Step-by-step explanation:

The formula for the slope is:

[tex]\frac{y2-y1}{x2-x1}[/tex]

Plug in (7,1) and (10, 3):

[tex]\frac{3-1}{10-7} = 2/3[/tex]

Answer:

25 miles

Step-by-step explanation:

Hakeem is starting a running plan to train for a race. In the first week of his running plan, Hakeem will run 11 miles. The plan calls for Hakeem to increase his weekly milage by 2 miles every week. If Hakeem sticks to the plan, how many miles would he be expected to run during his 8th week of the training plan?

This can be described as:

11 + 2w

when w = week

because he runs 11 miles the first week, he only has 7 weeks of 2 mile increases:

11 + 2(7) = 25 miles

Answer:

25/6

Step-by-step explanation:

We determine the scale factor by comparing the lengths of corresponding sides of the square. 
The length of O’N’=15 and the length of ¯¯¯¯¯¯¯¯¯¯¯ON=9

The equation for the scale factor, k is then given by:

O’N’=kON

15=9k

K= 15/9= 5/3.

The scale factor is k= 5/3

Hey you man what are you doing here go to there

We will compute the volume of each figure.

1) Figure A

We have a cone with:

• Ab = base area = 20 cm²,

• h = heigh = 5 cm.

The volume of the cone is:

2) Figure B

We have a cylinder with:

• Ab = base area = 20 cm²,

• h = heigh = 6 cm.

The volume of the cylinder is:

3) Figure C

We have an inclined cylinder with:

• Ab = base area = 20 cm²,

• h = heigh = 5 cm.

The volume of the inclined cylinder is:

4) Figure D

We have a parallelepiped with:

• Ab = base area = 20 cm²,

• h = heigh = 5 cm.

The volume of the parallelepiped is:

5) Figure E

We have an inclined square pyramid with:

• Ab = base area = 20 cm²,

• h = heigh = 10 cm.

The volume of the square pyramid is:

Answer

Among these figures, figure C and figure D have the same volume.

The theorem that proves that lines d and e are parallel is the: A. converse of the alternate exterior angles theorem.

The alternate exterior angles that are formed on each lines that are cross by the transversal are said to be congruent or equal to each other if both lines they lie on are parallel, based on the alternate exterior angles theorem.

Also, we can prove that if the alternate exterior angles are congruent, then the lines they lie on are parallel lines, using the converse of the alternate exterior angles theorem.

Thus, we are given that angle 2 = angle 6. Angles 2 and 6 lie on lines d and e. Since they are equal to each other, they are congruent angles. Therefore, lines d and e are parallel lines based on the converse of the alternate exterior angles theorem.

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Answer:

Midpoint formula is given as [(x1+x2)÷2, (y1+y2)÷2], where x and y are coordinates of the points.

Midpoint = [(19+17)÷2, (6+(-3))÷2]

= (36÷2, 3÷2)

= (18, 1.5)

Answer: 4/5

Step-by-step explanation:

y = mx + b

m represents the slope in this line.

Answer:

4/5

Step-by-step explanation:

Equation is in slope intercept form:

[tex]y = mx + b[/tex]

where m is the slope and b us the y-intercept

so, slope is 4/5

Answer:

125.

Step-by-step explanation:

5^3

= 5 * 5 * 5

= 25 * 5

= 125.

When the price is $1,500 for 1,080 square feet of carpet, the price per square feet is $1.389.

It should be noted that from the information, it was stated that the price is $1,500 for 1,080 square feet of carpet.

In this case, it should be noted that the price per square feet will be:

= Total amount / Number of square feet

= $1500 / 1080

= $1.389 per square feet.

Therefore, the price is $1.389.

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$1,500 for 1,080 square feet of carpet. Find the. price per square feet

can't understand Ur question nicely