1. (04.02)
What is the quotient when x³ - 5x² + 2x + 5 is divided by x - 2?

When comparing the means of two populations, it is often preferable to use a two-sample t test, rather than a one-way ANOVA f test because the non-pooled t statistic does not require the assumption that the populations have equal Variances.

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Answer:

x = 22/5; m∠TKW=m∠XHK = 15.2°

Step-by-step explanation:

Angles TKW and XHK are corresponding angles (as they lie on the same side of the traversal and on the bottom left side of their respective lines) and are thus congruent and equal.

By setting the two equations equal to each other, we can find the value.

After this, we can plug in x for any one of the equations and find the measure of both angles:

[tex]8x-20=3x+2\\8x=3x+22\\5x=22\\x=\frac{22}{5} \\\\TKW=8(\frac{22}{5})-20\\ TKW=\frac{176}{5}-20\\ TKW=\frac{76}{5}=15.2\\ TKW=XHK[/tex]

The blanks are filled as below

Collinear points are those that are situated along a single straight line.

Collinear points are those that are on a line either close to or far from another point, it can be more than two points.

While coplanar points imply lying on the same plane

In the diagram,

E, F, and G are collinear points

D, B, E, F, and G are coplanar points

A, B, and C are another collinear points

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Answer:

√130

Step-by-step explanation:

                              |

          ?                  |         7

                              |

---------------------------

            9

a² + b² = c²

7² + 9² = c²

49 + 81 = c²

130 = c²

√130 = √c²

√130 = c

I hope this helps!

Answer: Z=80

Step-by-step explanation:

The surface area of the rectangular prism is 18 sq cm greater than the surface area of the cube.

Here, we are given a rectangular prism and a cube as shown in the figure below.

The three sides of the prism are- 2, 3 and 6

Thus, the total surface area of the cube will be-

2 [(2*3) + (3*6) + (6*2)]

= 2[6 + 18 + 12]

= 2*36

= 72 cm square

Now, the side of the cube is 3 cm

Thus, the total surface area of the cube will be-

6( 3*3 )

= 6*9

= 54 cm square

Thus, the difference between the surface area of prism and cube is = 72 - 54

= 18 cm square.

Thus, the surface area of the rectangular prism is 18 sq cm greater than the surface area of the cube.

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Your question was incomplete. Check for the missing figure below.

The measure of the numbered angles are:

m ∠1 = 42°

m ∠2 = 48°

m ∠3 = 132°

m ∠4 = 90°

From the question, we are to determine the measure of each numbered angle.

From the given information,

Line l is parallel to line m and line PQ is perpendicular to line RQ.

Since line PQ is perpendicular to line RQ,

Then, we can write that

48° + m ∠1 = 90°

m ∠1 = 90° - 48°

m ∠1 = 42°

Also,

Since line PQ is perpendicular to line RQ,

m ∠4 = 90°

Since line l is parallel to line m,

m ∠2 = 48° (Alternate interior angles)

m ∠3 + m ∠2 = 180° (Linear pair theorem)

m ∠3 + 48° = 180°

m ∠3 = 180° - 48°

m ∠3 = 132°

Hence, the measure of angle 3 is 132°

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The length of the segment connecting (-4, 3) and (-5,2) is 1.4.

The length of a line segment can be measured by measuring the distance between its two endpoints.

Therefore, the length of the segment connecting (-4, 3) and (-5,2) can be found as follows:

length of the segment = √(2 - 3)² + (-5 + 4)²

length of the segment = √(-1)² + (-1)²

length of the segment = √1 + 1

length of the segment = √2

length of the segment = 1.41421356237

length of the segment = 1.4

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By using unitary method, it can be calculated that Height of the tree is 30 feet

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

This is a problem on unitary method

A shadow of 4.5 feet long is casted  by my friend 5 feet tall

A shadow of 1 feet is casted by an object of height [tex]\frac{5}{4.5} \ feet[/tex]

A shadow of 27 feet is casted by a tree of height [tex]\frac{5}{4.5}\times 27 \ feet[/tex]

A shadow of 27 feet is casted by a tree of height 30 feet

Height of the tree is 30 feet

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By using substitution method, x = 0, and y = -3 are the solutions of the given system of equations.

What is substitution method?

In order to solve a system of equations, the substitution approach is typically utilized in mathematics. The first equation involving the variable must be solved using this method before the variable's value is substituted in the second equation.

Consider the given system of equations

-5x - 3y = 9       ..(1)

4x - 18y = 54       ..(2)

From equation (1),

-5x = 9 + 3y

[tex]x =- \frac{9+3y}{5}[/tex]              ..(3)

Plug the value of x in equation (2),

[tex]4(-\frac{9+3y}{5})- 18y = 54\\-36-12y-90y = 270\\ -36 - 102y=270\\102y = -36-270\\102y=-306\\y = -3[/tex]

Plug y = -3 in equation (3)

[tex]x = -\frac{9+3(-3)}{5} =-\frac{9-9}{5} =0[/tex]

x = 0

Hence, by substitution method x = 0 and y = -3.

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Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.

What is unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

According to the given question:

Gianna can wash 6 cars in 2 hours

Therefore, in 1 hour she can wash 6/2 cars which is 3 cars.

Gianna's rate of washing cars is 3 cars per hour

Hence by unitary method, Gianna at this rate can washes 5 x 3 cars that is 15 cars.

Gianna washes 15 cars in 5 hours as her rate of washing cars is 3 cars per hour.

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The number of miles Melissa travelled that night is approximately 667 miles.

Melissa is planning to rent out a limo for her friends and herself for prom.

Limousine rates charge a 450 flat rate plus an additional 30 cents for every mile travelled.

Melissa aid the limousines driver $200 for prom. The number of miles she travel can be calculated as follows;

using equation,

y = 450 + 0.3x

where

Therefore,

200 + 450 = 450 + 0.3x

650 = 450 + 0.3x

650 - 450 = 0.3x

200 = 0.3x

x = 200 / 0.3

x = 666.666666667

x = 667 miles

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Standard form of ellipse has equation [tex]\frac{y^2}{a^2} +\frac{x^2}{b^2} =1[/tex] where, a and b are the halves of the length of major and minor axis respectively.

Given that,

Length of major axis(2a)=6.

So

a=6/2

 =3

Length of minor axis(2b)=4.

So

b=4/2

 =2

Putting in equation of standard ellipse. We get

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

After simplifying

4y² + 9x² = 36

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Using the Pythagorean Theorem, the number of feet from the tent pole to the rope along the ground is 12 feet.

In the given question we have to determine the number of feet from the tent pole to the rope along the ground.

From the question;

A tent pole that is 5 feet tall is secured to the ground with a piece of rope that is 13 feet long from the top of the tent pole to the ground.

So the value of Hypotenuse(H) = 13 feet

Perpendicular(P) = 5 feet

Using the Pythagorean Theorem

H^2=P^2+B^2

Putting the value

(13)^2=(5)^2+(B)^2

169 = 25+B^2

Subtract 25 on both side, we get

B^2=169-25

B^2=144

Taking square root on both side, we get

B=12

Hence, the number of feet from the tent pole to the rope along the ground is 12 feet.

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Answer:

B: (5,3)

Step-by-step explanation:

We just fill in the coordinates

A: (7,9)

9=7-2

9=5

not true

B: (5,3)

3=5-2

3=3

true

C: (7,14)

14=7-2

14=5

not true

D: (5,7)

7=5-2

7=3

not true

so b is the only correct answer

hopes this helps please mark brainliest

A) The number of pounds that the beverage cans are recycled in an hour is 119772 pounds

B) The number of tons that the beverage cans are recycled in an average day is 2397 ton

C) The number of Kilograms that the beverage cans are recycled in a day is 57528000 kg

The pound is the main unit of sterling, and the term "pound" is frequently used to refer to British currency in general, which is often qualified in foreign contexts as the British pound or the pound sterling.

In 2002 about 34 beverages can weigh one pound.

In one minute 113204 beverage cans are recycled.

In one hour, 60 minutes number of beverage cans recycled=113204×60

=6792240

34 beverage cans weight 1 pound

1 beverage cans weight=1/34 pounds

A) 6792240 beverage can weigh=1

=(1/34)(6792240) pound

=119771.765 pound

≈119772 pound

B) So, In 24 hours, no. of pounds recycled

=119772×24 pound

=119772×24×0.0005 ton

=2397.26 ton

≅2397 ton in one day.

C) So, In 24 hours, no. of tons recycled

=2397×24 ton

=2397×24×1000 kg

=57528000 kg

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Clearly,  it is a reduction with scale factor 2

The rightmost line of the black figure has  8 units and pink has 4 units similarly the first horizontal link of black has 4 while pink has 2 units. By labeling the sides of both figures and finding the ratio of the sides of the black figure to the pink figure is 2 so it is deduced that the scale factor is 2 and its reduction as black figure is an enlargement of pink.

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The pink figure is a dilation image of the black figure. The labeled point is the center of dilation. The dilation is a reduction with scale factor 2.

In mathematics, dilation means Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. The size of the form does differ, though.

The rightmost line of the black figure has  8 units and pink has 4 units similarly the first horizontal link of black has 4 while pink has 2 units. By labeling the sides of both figures and finding the ratio of the sides of the black figure to the pink figure is 2 so it is deduced that the scale factor is 2 and its reduction as black figure is an enlargement of pink.

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The Height of trees are equal after 4 years and the height is 54 inches.

A linear equation is a equation which draws straight line on the plot

when plotted.

Given,

Height of tree A at the time of planting = 38 inches

Height of tree B at the time of planting = 22 inches

Each year  tree A grow = 4 inches

Each year  tree B grow = 8 inches

Let's make an equation for the height of the trees,

H = 38 +4t

H = 22+8t

Now the time when height of both the trees will equal

38 + 4t = 22 + 8t

4t = 16

t = 4

Hence , After 4 years the height of both the trees will equal and the height of both the trees after 4 years will be 54 inches.

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They both Bihn and Inscoe can do same work in 3(1/13) hours.

How to solve work time problems?

Efficiency = (work)/(time)

Bihn can write one test =  Eight hours

Bihn's one hour work = 1/8

Inscoe can write one test = Five hours

Inscoe's one hour work = 1/5

Bihn and Inscoe 's one hour work =  1/8 + 1/5

= (5 + 8)/40

= 13/40

Both Bihn and Inscoe can do same work in 40/13

= 3(1/13) [13 * 3 + 1]

Hence, they both Bihn and Inscoe can do same work in 3(1/13) hours.

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Answer: It is A

Step-by-step explanation:

Answer:

C. $4.00

Step-by-step explanation:

Profit, which is given by [tex]P(x)[/tex], is maximized when the price per drink is $4.00, as shown on the graph.

The measurement of angle DBC is 100°. It can be obtained by the properties of bisector of an angle and algebriac multiplication.

What is angle bisector?

An angle bisector is the ray or line segment that divides the angle into two equal parts.

Since the segment BD bisects angle ABC hence,

∠ABC = ∠ABD+∠DBC               ..... (1)

Also, since segment BD bisects angle ABC hence,

∠ABD = ∠DBC

Use this fact in equation (1)

∠ABC = ∠ABD+∠ABD

∠ABC =2 ∠ABD

Now, substitute values and use algebriac multiplication.

7x = 2(3x+25)

7x = 6x+50

7x - 6x= 50

x=50

Now, substitute the value of x in the expression of ∠ABD.

∠ABD = 3x+25

∠ABD = 3(50)+25

∠ABD = 100

Now, since ∠ABD = ∠DBC hence, ∠DBC = 100.

Hence, the measurement of angle DBC is 100°.

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The set of ordered pairs which represents a function as required in the task content is; { (-2, 0), (-5, -5), (-1, 3), (2, 0) }.

It follows from the task content that the set of ordered pairs which represents a function is to be identified among the answer choices.

It is noteworthy to know that a function is a special kind of relation in which case each input value is assigned only one output value.

Put simply, no one input value has more than one output value assigned to it.

On this note, the answer choice which correctly represents a function among the answer choices is; { (-2, 0), (-5, -5), (-1, 3), (2, 0) }.

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The marked-up price of the desk in the furniture store is $158.92.

The markup is the difference added to the cost of a product or service.

The markup represents the seller's profit on the cost.

The markup differs from the margin, which is the ratio of the seller's profit to the sales price.

The wholesale price of a desk = $137

Markup rate = 16%

Marked-up price = $158.92 ($137 x 1.16)

Thus, the desk is sold at the marked-up price of $158.92.

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Answer:

a₁ = -27

a₂ = -32

a₃ = -37

a₄ = -42

a₅ = -47

a₅₂ = -282

Step-by-step explanation:

An explicit formula for an arithmetic sequence allows you to find the nth term of the sequence.

Given explicit formula:

[tex]a_n=-5n-22[/tex]

To find the first 5 terms, substitute n = 1 through 5 into the given formula:

[tex]\begin{aligned}\implies a_1&=-5(1)-22\\&=-5-22\\&=-27\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_2&=-5(2)-22\\&=-10-22\\&=-32\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_3&=-5(3)-22\\&=-15-22\\&=-37\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_4&=-5(4)-22\\&=-20-22\\&=-42\end{aligned}[/tex]

[tex]\begin{aligned}\implies a_5&=-5(5)-22\\&=-25-22\\&=-47\end{aligned}[/tex]

To find the 52nd term, substitute n = 52 into the given formula:

[tex]\begin{aligned}\implies a_{52}&=-5(52)-22\\&=-260-22\\&=-282\end{aligned}[/tex]

the diameter to allow an elongation of 0. 38 mm therefore required diameter is 7.65 mm

Given the data in the question;

F = 11100 N

l₀ = 310 mm = 0.31 m

E = 207 GPa = 207 × 10⁹ N/m²

Δl = 0.38 mm = 0.0005 m

So, lets assume the deformation is elastic;

d₀ = √(  [4l₀F] / [πEΔl] )

we substitute

d₀ = √(  [4 × 0.38 × 11100] / [π × (207 × 10⁹) × 0.0005]] )

d₀ = √( 10123.2 / 172787595.947 )

d₀ = √( 5.85875 × 10⁻⁵ )

d₀ = 0.007654 m

d₀ = ( 0.007654 × 1000 )mm

d₀ = 7.65 mm

Therefore, required diameter is 7.65 mm

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