!!30 Points, Pls help ASAP!!
Divide using synthetic division
x^4 – 3x^3 – 7x + 1 ÷ x + 2

Answer:

x = 20

y = 70

Step-by-step explanation:

It's rather difficult to explain since nothing is labeled but those are the answers

The volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.

What is a rectangular Prism ?

A polyhedron with two congruent and parallel bases is known as a rectangular prism. It's also known as a cuboid.

A rectangular prism has six faces, each of which is in the shape of a rectangle and has twelve edges. It's called a prism because of its cross-section along its length.

It is given that length of the rectangular prism has length of 2 cm more than  the width and 3 cm less than the depth

Let the depth be x cm

and width be y cm

Then the length will be y+2 cm and x-3 cm

y+2 = x- 3

x = y+5

A rectangular prism is a cuboid with six faces

Volume of a rectangular prism can be written as

length * width * depth

= (y+2) *x*y

= (y+2)* (y+5)*y

= (y²+2y)(y+5)

= y³ +5y²+2y²+10y

= y³ +7y² +10y cm³

Therefore the volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.

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Slope of the line is .[tex]\frac{-4}{3}[/tex]

Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. As opposed to the net change in the x coordinate, the net change in the y coordinate is y.

y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

A line's slope is a measurement of how steep it is or the direction it is going in relation to a coordinate system.

where m is the slope and m = y/x

Take notice that tanФ = y/x.

This tanФ is often referred to as the line's slope.

The given equation is of the form [tex]ax+by=c[/tex]

On comparing we can say that a is -8 and b is -6

So using the slope formula [tex]\frac{-A}{B}[/tex] we get slope as [tex]\frac{4}{-3}[/tex]

The perpendicular line slope can be found out by equation [tex]m1.m2=-1[/tex]

Therefore substituting slope from the above as m1 we get m2 = [tex]\frac{3}{4}[/tex]

Slope of the line is .[tex]\frac{-4}{3}[/tex]

Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]

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Answer:

Breadth = 10 ft

Step-by-step explanation:

Given information,

→ Perimeter (P) = 50 ft

→ Length (L) = 15 ft

→ Breadth (B) = ??

Now we have to,

→ find the required value of Breadth.

Formula we use,

→ P = 2(L + B)

Then the required Breadth will be,

→ P = 2(L + B)

→ 50 = 2(15 + B)

→ 30 + 2B = 50

→ 2B = 50 - 30

→ B = 20/2

→ [ B = 10 ft ]

Hence, required Breadth is 10 ft.

Answer:

Negative seven and seven sixteenths

Step-by-step explanation:

2⅛ x (-7) x 5/10

= 17/8 x (-7) x 1/2

= - 119/16

= - 7 7/16

The perimeter of the image is 70 meters and its area is 210 square meters.

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.

There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter.

Area=(1/2)×base× height

=(1/2)×21×20

=210 square meters

Perimeter=a+ b+ c

=21+20+29

=70meters

Therefore, The perimeter of the image is 70 meters and its area is 210 square meters.

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The house that they will first meet if a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house is the 24th house.

The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers, or lcm(a, b), in mathematics and number theory. Since the result of dividing an integer by zero is undefinable, this definition only applies if both a and b are not equal to zero.

Before fractions can be added, subtracted, or compared, the "lowest common denominator" can be employed.

From the information, a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house.

It should be noted that this will be illustrated through tye lowest common multiple.

Multiples of 6 = 6, 12, 18, 24

Multiples of 8 = 8, 16, 24

Therefore, they'll meet at the 24th house.

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Answer:

5

Step-by-step explanation:

The logarithm function, denoted as "log," is the inverse of the exponentiation function. This means that if we have the expression "log(x) = y," then "x" is the base "b" raised to the power "y." In other words, "x" is equal to "b^y."

Using this definition, we can simplify the expression "10^log5" as follows:

10^log5 = 10^y

Where "y" is the exponent to which the base "10" must be raised to produce the result "5."

To find the value of "y," we can use the property of logarithms that states "log(b^y) = y." Applying this property to our expression, we have:

log(10^y) = y

Since "10^y" is equal to "5," we can substitute "5" for "10^y" in the above equation:

log(5) = y

Solving for "y," we find that "y = log(5)."

Therefore, the expression "10^log5" can be simplified to:

10^log(5) = 10^(log(5)) = 5

So the simplified result is 5.

Answer: 15/16 hour

Step-by-step explanation:

The unidentified term is 3m.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, an equation (x-0.2n)² = x-1.2mn+0.04n²

We know that, (a-b)² = a²-2ab+b²

Comparing the given equation with the above identity, we get,

a = x, b = 0.2n and 2ab = 1.2mn

Therefore, 2x×0.2n = 1.2mn

x = 3m

Hence, the unidentified term is 3m

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Answer:

$1944

Step-by-step explanation:

18x12=216

216x$9=$1944

Answer:

£1944

Step-by-step explanation:

The area of the floor is 216 feet²

18 x 12 = 216

216 x 9 = 1944

Answer: 22( w + 2 ) =77 and the amount of the water bottle would be 1.50

Step-by-step explanation: i dont know what to write??

Answer:

22

Step-by-step explanation:

Corresponding sides of similar triangles are proportional.

[tex]\frac{3x+2}{5x-4}=\frac{15}{20}=\frac{3}{4} \\ \\ 12x+8=15x-12 \\ \\ 3x=20 \\ \\ \therefore SP=20+2=22[/tex]

Answer:

[tex]A \approx 38 \, \textrm{cm}^2[/tex]

Step-by-step explanation:

The area of a triangle is defined as:

[tex]A_\triangle = \dfrac{1}{2}bh[/tex]

where [tex]b[/tex] is the length of its base and [tex]h[/tex] is its height.

So, we can plug the given values into this formula along with the inch to centimeter conversion to get the answer to this problem.

[tex]A=\dfrac{1}{2}\left(4.75\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)\left(2.5\, \textrm{in} \times \dfrac{2.54 \, \textrm{cm}}{1 \, \textrm{in}}\right)[/tex]

And simplify.

[tex]A \approx 38 \, \textrm{cm}^2[/tex]

Since the line is linear, the sum of the angles should be 180 degrees

x + 28 + 73 = 180

x = 180 - 28 - 73

x = 79 degrees

Hope this helped :)

Either the slope intercept form or the point-slope form can be used to express the equation of a line-, the line's equation is - 3x - 5.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two distinct points on a line can be used to calculate the slope of any line.

The ratio of "vertical change" to "horizontal change" between two different points on a line is calculated using the slope of a line formula.

According to our question-

the points are given as

(x1,y1)=0,-5

(x2,y2)=-3,4

m = y2-y2/x2-x2

Hence, the line's equation is - 3x - 5.

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Answer:

5/13

Step-by-step explanation:

[tex]CE=\sqrt{10^2 + 24^2}=26 \\ \\ \cos E=\frac{10}{26}=\frac{5}{13}[/tex]

Answer:

5x + 16

Step-by-step explanation:

First you have to distribute the 2 into the parentheses

2 times x is 2x

2 times 6 is 12

so now the equation is

2x + 12 + 3x + 4

add the 2x and 3x and that is 5

so now the equation is...

5x + 12 + 4

add 12 + 4 and that is 16

so now the answer is

5x + 16

The value of x and z are [tex]4^\circ, 96^\circ[/tex].

Now from the picture I can say that, [tex]\angleAOB[/tex][tex]\angle AOB[/tex] and [tex]\angleCOD[/tex][tex]\angle COD[/tex] are opposite angles.

We know the measure of the triangle are equal in Pair.

So we have got the equation as -

[tex]10x+44=13x+32[/tex]

⇒[tex]13x-10x=44-32[/tex]

⇒3x=12

⇒x=4.

We have got that the measure of [tex]\angle AOB, \angle COD[/tex] are both [tex]84^\circ[/tex].

Now angles around a point add to [tex]360^\circ[/tex].

So, [tex]\angle AOD[/tex] and [tex]\angle BOC[/tex] are equal since they are pairwaite wisw.

Now, [tex]z+z= 360^\circ - (84^\circ+84^\circ)[/tex]

⇒[tex]2z=192^\circ[/tex]

⇒ [tex]z=96^\circ[/tex],

Hence we have got the value of x and z i.e. 4 and 96.

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The value of the side AC is 40 if the points  B, D, and F are midpoints of

the sides of ΔACE.

The midpoint theorem states that in order to determine the midpoints of a triangle's sides, "a line segment linking any two of its midpoints is said to be parallel to the triangle's third side and also half the length of the third side."

Divide the distance between the two endpoints by 2, then do it again. The two terminal x coordinates can alternatively be combined, then the result divided by two. Draw a line from a midway to the opposite corner. The centroid of a triangle is the point at where the three medians intersect.

Given,

The points B, D, F are midpoints of the sides of a triangle ACE.

And also given that,

EC =32 and DF=20, AC=?

So, FD=1/2(AC)

AC=2(FD)

AC=2(20)

AC=40

Therefore, the value of the side AC is 40 if the points  B, D, and F are

midpoints of the sides of ΔACE.

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The value of n when is divided by 6 and it gives 42 is 252

Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division and 12 divided by 4 gives 3 in each group. This means that 3 and 4 are factors of 12

When dividing a number by another number that is not it's factor, there will be remainder for example 12 divided by 5 . It will give 2 remainder 2. This is because 5 is not a factor of 12.

Similarly, n divided by 6 to give 42. This means that 42 and 6 are factors of n

Therefore to find n we multiply 42 and 6.

n = 42×6

n = 252

therefore the value of n is 252

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Answer:

congruence is compatibility or agreement while equal is the same or equivalent to one another.

Answer:

x ≥ 5

Step-by-step explanation:

5 + 2 (2x - 3) ≥ 3x + 4

5 + 4x - 6 ≥ 3x + 4

-1 + 4x ≥ 3x + 4

4x ≥ 3x + 5

x ≥ 5

The conditional probability that a randomly-generated 4-bit string contains two consecutive 1s is 3 / 8 .

total length of four-bit strings = 16

Let S represent the collection of all four-bit bit strings.

Let A represent the occurrence of a randomly generated string beginning with 1.

Let B represent the scenario where a string created at random contains two consecutive 0s.

S has 8 strings that begin with the letter "1."

P( A ) = 8 / 16 = 1 / 2

Strings in S starting with 1 and having two consecutive zeros are 1000 , 1001 , 1100

P(A ∩ B)  = 3 / 16

Conditional probability that at least two consecutive 0s will appear in a randomly generated bit string of length four is ,

3/16 / 1/2

= 3 / 8

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Answer:

photo?

Step-by-step explanation:

There is 20% decrease in the number of people who went to the pool over these four weeks.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

There is no dimension to percentages. As a result, it is known as a dimensionless number. When we say a number is 50% of anything, we mean that it is 50% of everything.

Attendance of pool in first week of July = 1120

In second week, 125 fewer people joined.

Thus, attendance in second week is = 1120-125 = 995

In third week, 130 more people joined.

Thus, attendance in third week is = 995+130 = 1125

In fourth week, 229 fewer people joined.

Thus, attendance in fourth week is = 1125-229 = 896

Difference of attendance in first and fourth week = 1120-896 = 224

Percentage decrease = (Decrease number/Initial number)×100%

= (224/1120)×100%

= 0.20×100%

= 20%

Thus, there has been a 20% decrease over the four weeks.

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So the valid bounding conditions for the sum of the subset problem are:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

The valid bounding condition for the sum of the subset problem is:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

This means that each item can either be included in the subset (x[i] = 1) or not included in the subset (x[i] = 0).

The sum of the weights of the items in the subset should not exceed the maximum capacity constraint, m. So the bounding condition for the weight of the subset is:

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

This means that the sum of the weights of the items in the subset should be less than or equal to the maximum capacity constraint.

So the valid bounding conditions for the sum of the subset problem are:

0 <= x[i] <= 1 (for all i such that 1 <= i <= n)

∑(w[i] * x[i]) <= m (for all i such that 1 <= i <= n)

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The equation that gives the relationship between cost (c) and area (a) is c = 2a

A variation is a relation between a set of values of one variable and a set of values of other variables

Given that: the cost (c) to paint a building varies directly with the area of the surface being painted (a) in square feet

We can write:

c α a

c = ka

where k is the constant of proportionality

since c = $3,000 and a = 1500

c = ka

3000 = 1500k

k = 3000/1500

k = 2

Thus, the equation of the relationship is c = 2a

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The final answer is that the probability of rolling a six sided die six times and having all numbers from 1 through 6 appear once in any order is 1.54.

This is calculated by probability of independent events.

We know that any die can get any of the six sides and all the throws are independent, so their intersection is given by the product.

So, P(A and B occurring together )= P(A)P(B) if A and B are independent.

And the probability of the throws i.e. the no. of ways every throw gets a unique number is (6/6) x (5/6) x (4/6) x (3/6) x (2/6) x (1/6)

This is because, being the probability of independent events , they are multiplied.

so, the total probability is 6.5.4.3.2.1/6^6 = 1.54

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