Divide.
(2x³ − 3x² + 5) ÷ (x − 4)

Answer:

Step-by-step explanation:

If the line is perpendicular to y = -2x + 5 then the new line has a slope of 1/2.

So solve for b: using y = mx + b

2 = 1/2(-4) + b

2 = -2 + b

4 = b

Put it all together

y = 1/2x + 4

The diameter of his circular field is 18miles

What is sprinkler?

A sprinkler irrigation system is a tool used to irrigate (water) lawns, gardens, golf courses, and other areas. They are also utilised for cooling and dust control in the air. Sprinkler irrigation is a technique for applying water in a way that is similar to rainfall: it is controlled. Pumps, valves, pipes, as well as sprinklers are just a few of the possible components of the network used to distribute the water. Sprinklers for irrigation can be used in residential, commercial, and agricultural settings. Both sandy soil and uneven terrain with insufficient water supply can benefit from it. The rotating nozzle-topped perpendicular pipes are linked to the main pipeline at regular intervals. Water leaks from the rotating nozzles when it is pressurised and forced through the main pipe.

The irrigation sprinkler in this instance is angled.

θ = 50 = 50 π/ 180 rad.

It mists a sphere-shaped area.

A = 2/(2 miles).

If the sprinkler's length is

miles, L. It will be watered within the circle's radius.

Hence,

L^2 = A when divided by two in radians.

⇒ L = √ (2 A / θ)

= √ [(2 x 2 x 180) /40 π]

≈ 18 miles

Hence, The diameter of his circular field is 18 miles

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There are 32 outfits that Evelyn can make.

This is basic combination.

Evelyn has 2 shirts each shirt can be worn with each of the 2 pair of pants.

So, there are 4 ways to wear them.

she  also has 8 pairs of shoes and each pair can be worn with each of the 4 outfits.

total number of outfits that she can make = 8*4

                                                                      =32 outfits

Evelyn can make 32 different outfits.

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Answer:

7

Step-by-step explanation:

The expression to represent the area of the rectangle is A = 6w⁷

The rectangle is a four-sided polygon with an internal angle of 90° at the corner of every side. The opposite sides of the rectangle are equal.

The formula for the area of the rectangle is given below

Area = Length × width

Here we have

Width of the rectangle = 3w² and

Length of the rectangle = 2w⁵

As we know the area of the rectangle = Length × width

Area of the rectangle, A = 3w² × 2w⁵

=> A = 6w²×w⁵

=> A = 6w²⁺⁵

=> A = 6w⁷

Therefore,

The expression to represent the area of the rectangle is A = 6 w⁷    

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The correct statement regarding the sentence square root of 49 = 7 is given as follows:

C. 7 is the length of the side of a square whose area is 49.

Considering a square of side length s, we have that the area and the perimeter of the square are given as follows:

In the context of this problem, the expression is given as follows:

square root of 49 = 7.

For a square with area of 49 units squared, the side length is obtained as follows:

s² = 49

s = square root of 49

s = 7.

Which means that option C is the correct option.

The problem is given by the image shown at the end of the answer.

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As per the given ratio, the length of the actual counter is 120 feet.

Ratio:

Basically, the ratio refers an ordered pair of numbers a and b, written a / b where b does not equal 0. And a proportion is an equation in which two ratios are set equal to each other.

Given,

Gwen measured a kitchen and made a scale drawing. The scale she used was 11 inches : 5 feet.

Here we need to find the length of the actual counter if  a countertop in the kitchen is 22 inches long in the drawing.

While looking into the given question, we have identified the following things,

Scale drawing ratio = 11 inches : 5 feet

And the length of the drawing = 22 inches.

When we convert the inches into feet,

Then we get,

=> 11 inches = 11/12 feet.

So the actual length can be calculated as,

=>22 : 11/12 : 5

=> 22 x 12/11 x 5

=> 2 x 12 x 5

=> 120

Therefore, the length of the actual counter is 120 feet.

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A Paired t-test evaluates data from dependent samples in which the two treatments are applied to the same individual.

T-test is a statistical statistics mainly use when population variance is unknown and sample size is small.

In Paired t-test , we compare means of two dependent samples . It gives hypothesis examination on difference between of mean.

It uses same items or people in both sample that's why they are also known as dependent t-test

Paired t-test also increases the statistical power of our analysis.

Formula of paired t-test :

[tex]t = \frac{m}{s/\sqrt{n} }[/tex]  with (n-1) degree

where , m is mean difference

s is standard deviation

n is sample size

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Weak positive term describes the correlation  .

What does a weak positive indicate?

A weak positive graph is what?

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Answer:

11:8

3:11

Step-by-step explanation:

The total is 11 (3+ 8)

Answer: B: -4

Step-by-step explanation: -168/-14 = 12

12/-3 = -4

The correct option is option (C) .

Cluster Sampling is a type of probability sampling and other options are non- probability sampling examples .

Sampling :

Sampling is defined as a technique that selects individual members or subsets from a population to help determine characteristics of the population as a whole.

Croach and Housden postulate that a sample is a finite number taken from a large group for testing and analysis, and that the sample can be taken as representative of the group as a whole.

There are two main types of sampling:

i) probability sampling

ii) Non-probability sampling

A) probability sampling:

It is defined as the sampling technique which researchers use a related method to draw probability theory samples from a larger population.

The most important requirement for probabilistic sampling is that everyone in the population has a known equal chance of being selected.

Probability Samples:

1. Stratified Sampling: Stratified sampling is a type of sampling technique that divides the total population into smaller groups or strata to complete the sampling process. Hierarchies are formed based on some common characteristics of demographic data.

2. Cluster Sampling: Cluster sampling is a probabilistic sampling technique in which researchers divide a population into multiple groups (clusters) for research purposes. Researchers then select random groups using simple sampling techniques for data collection and data analysis.

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The reflection of the point K across the y-axis is (5, -5)

From the question, the point is given as:

Point K = (-5, -5)

Rewrite this point as

K = (-5, -5)

The transformation is given as

Reflection across the y-axis

Mathematically, this transformation can be represented as

(x, y) = (-x, y)

So, we have

K' = (5, -5)

Hence, the image of the reflection is (5, -5)

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Answer:

(5, -5)

Step-by-step explanation:

The other guy is 100% right!

Answer:

Speed at which Carley was cycling at

= 72 miles ÷ 3 hours

= 24 miles/hour

Speed at which Catie was driving at

= 132 miles ÷ 2 hours

= 66 miles/hour

66 miles/hour - 24 miles/hour = 42 miles/hour

∴ The faster person, Catie, was travelling 42 miles/hour faster than Carley, the slower person.

Answer:

Step-by-step explanation:

The given translates as:

Use given x - intercepts to get the equation:

Use the coordinates of P to find the value of a:

The equation of this parabola is:

Answer:

[tex]\textsf{Intercept form}: \quad y=\dfrac{2}{5}(x-5)(x-12)[/tex]

[tex]\textsf{Standard form}: \quad y=\dfrac{2}{5}x^2-\dfrac{34}{5}x+24[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

If the x-intercepts are (5, 0) and (12, 0) then:

Substitute the values of p and q into the formula:

[tex]\implies y=a(x-5)(x-12)[/tex]

To find a, substitute the given point on the curve P (7, -4) into the equation:

[tex]\implies -4=a(7-5)(7-12)[/tex]

[tex]\implies -4=a(2)(-5)[/tex]

[tex]\implies -4=-10a[/tex]

[tex]\implies a=\dfrac{-4}{-10}[/tex]

[tex]\implies a=\dfrac{2}{5}[/tex]

Substitute the found value of a into the equation:

[tex]\implies y=\dfrac{2}{5}(x-5)(x-12)[/tex]

Expand to write the equation in standard form:

[tex]\implies y=\dfrac{2}{5}(x^2-17x+60)[/tex]

[tex]\implies y=\dfrac{2}{5}x^2-\dfrac{34}{5}x+24[/tex]

Answer: y = 4x + 7

Step-by-step explanation:

It's a line, so the formula is y = mx + b.

Slope(m): [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}} =\frac{-1-3}{-2-(-1)} =\frac{-4}{-1} =4[/tex]

Y-intercept(b):

[tex]y=4x+b\\3=4(-1)+b\\3=-4+b\\b=3+4=7\\[/tex]

Therefore, y = mx + b = 4x + 7.

The side lengths of the triangle is 17, 144, 145

Let x be the length of the short leg

The length of the longer leg of a right triangle is 25 cm more than seven times the length of the shorter leg

The length of the long leg is 25 + 7x

The length of the hypotenuse is 26 cm more than seven times the length of the shorter leg.

The length of the hypotenuse is 26 + 7x

(26 + 7x)² = (25 + 7x)² + x²

676 + 364x + 49x² = 625 + 350x + 49x² + x²

0 = x² -14x - 51

0 = (x - 17)(x + 3)

{-3, 17}

Length cannot be negative.

The length of the long leg is 25 + 7x = 25 + 7(17) = 144

The length of the hypotenuse is 26 + 7x = 26 + 7(17) = 145

Therefore, the side lengths of the triangle is 17, 144, 145

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Answer:

answer is 5

Step-by-step explanation:

Answer: Angles 1, 3, 7

Step-by-step explanation:

∠7 is vertical to ∠5

∠1 is corresponding to ∠5

∠3 is opposite interior angle of ∠5, it is also vertical to ∠1

Answer:

Step-by-step explanation:

First Selling price is $360, after mark down.

The second's selling price is $403, after both mark downs

Joanne should buy the first, because of the selling price after mark downs.

By using the concept of rate of change, it is obtained that

Water level is falling at the rate of [tex]\frac{2}{9\pi}[/tex] m per minute

What is rate of change?

Suppose there is a function and there are two quantities. If one quantity of a function changes, the rate at which other quantity of the function changes is called rate of change of a function.

Here the concept of rate of change has been used

Let the radius of cone at any point be r m and height be h m

Volume of cone = [tex]\frac{1}{3}\pi\times r^2\times h[/tex]

Now,

By the concept of similarity,

[tex]\frac{r}{h} = \frac{4}{16}\\\\\frac{r}{h} = \frac{1}{4}\\\\r = \frac{1}{4}h[/tex]

Volume of cone (V) =

[tex]\frac{1}{3}\times \pi \times (\frac{1}{4} h)^2\timesh\\\\\frac{1}{48}\times \pi \times h^3\\[/tex]

[tex]\frac{dV}{dt} = \frac{1}{48} \times \pi \times 3h^2\times \frac{dh}{dt}\\\\\frac{dV}{dt} = \frac{1}{16} \times \pi \times h^2\times \frac{dh}{dt}\\\\[/tex]

Now,

[tex]\frac{dV}{dt} = -2,\ h = 12[/tex]

So,

[tex]-2 = \frac{1}{16}\times \pi \times (12)^2 \times \frac{dh}{dt}\\\\\frac{dh}{dt} = -\frac{2 \times 16}{\pi \times 12 \times 12}\\\\\frac{dh}{dt} =- \frac{2}{9\pi}[/tex]

So water level is falling at the rate of [tex]\frac{2}{9\pi}[/tex] m per minute

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Answer: $617.50

Step-by-step explanation:

9.5% of 6500 = 9.5*6500/100=9.5*65=617.5

So the interest is $617.5 or $617.50

Hope this helped. If you have any questions or clarifications please ask.

Thanks and please rate!

Answer:

Gretta will earn $617.50 interest

A = $7,117.50

Equation:

A = P(1 + rt)

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 9.5%/100 = 0.095 per year.

Solving our equation:

A = 6500(1 + (0.095 × 1)) = 7117.5

A = $7,117.50

The total amount accrued, principal plus interest, from simple interest on a principal of $6,500.00 at a rate of 9.5% per year for 1 years is $7,117.50.

The average of the given 5 equations is; x' = 2x - 1.6

In mathematics, average is also called the mean and it has the formula as;

x' = ∑fx/∑f

Now, we are given the equations as;

x + 3, 2x - 4, 3x - 6, 2x - 5, and 2x.

Thus;

∑fx = x + 3 + 2x - 4 + 3x - 6 + 2x - 5 + 2x

∑fx = 10x - 8

The number of expressions given is 5 and so ∑f = 5

Thus;

x' = (10x - 8)/5

x' = 2x - 1.6

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The values of the segments formed by the median lines in the triangles are;

1. KG = 22

2. [tex]\overline{JE}[/tex] = 19.5

3. FL = 11

9) CI = 4

10) XK = 4

14) x = 3

A median line of a triangle is a line drawn from a vertex of the triangle to the the middle of the of the opposite side, thereby bisecting the opposite side into two segments of the same length.

The median lines are; [tex]\overline{JE}[/tex], [tex]\overline{KF}[/tex], and [tex]\overline{LD}[/tex]

1. The length of [tex]\overline{GF}[/tex] = 11

The properties of a median line indicates;

[tex]\overline{GF}[/tex] = (1/3)·[tex]\overline{KF}[/tex]

Therefore;

11 = (1/3)·[tex]\overline{KF}[/tex]

[tex]\overline{KF}[/tex] = 3 × 11 = 33

[tex]\overline{KG}[/tex] = (2/3)×[tex]\overline{KF}[/tex]

Therefore;

[tex]\overline{KG}[/tex] = (2/3) × 33 = 22

[tex]\overline{KG}[/tex] = 22

2. [tex]\overline{JG}[/tex] = 13

[tex]\overline{JG}[/tex] = (2/3) × The median line [tex]\overline{JE}[/tex]

Therefore;

[tex]\overline{JG}[/tex] = (2/3) × [tex]\overline{JE}[/tex]

[tex]\overline{JE}[/tex] = (3/2) × [tex]\overline{JG}[/tex]

[tex]\overline{JE}[/tex] = (3/2) × 13 = 19.5

3. JL = 22

[tex]\overline{KF}[/tex] is a median line, therefore, the point F is the midpoint JL

JF = FL

JL = JF + FL by segment addition postulate

JL = FL + FL = 2·FL (substitution property of equality)

JL = 22 = 2·FL

FL = 22 ÷ 2 = 11

9) CS = 6

Where CS is a median line of the triangle ΔABC, then;

CI = (2/3) × CS

CI = (2/3) × 6 = 4

10) UX = 8

Where UX is a median of the triangle ΔTUX, we get;

XK = (1/3) × UK

UX = (2/3) × UK

UK = (3/2) × UX = (3/2) × 8 = 12

XK = (1/3) × 12 = 4XK = 4

14) KL = 7·x + 1

LE = 2·x + 5

The properties of median line indicates that, KL = (2/3)·KE

LE = (1/3)·KE

Therefore;

KL = 2 × LE

7·x + 1 = 2 × (2·x + 5) = 4·x + 10

7·x + 1 = 4·x + 10

7·x - 4·x = 10 - 1 = 9

3·x = 9

x = 9 ÷ 3 = 3

x = 3

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The P∩V is {2,4,6,8}.

From the question, we have

P= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

V= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

P∩V = {2,4,6,8}

Intersection of Sets:

The set that contains all the elements that are shared by two given sets is the intersection of the two sets. The intersection of sets is represented by the symbol "∩". The intersection A∩ B (also written as A intersection B) lists all the elements that are shared by any two sets A and B that are present in both sets.

For instance, if Set A = 1, 2, 3, 4, and Set B = 3, 4, 6, then A ∩B = {3,4}.

Complete question:

Suppose P = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and V = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}. what is P ∩ V ?

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Answer:

blood vessels

Step-by-step explanation:

Blood vessels carry nutrients throughout your body

Answer:

Step-by-step explanation:

the answer is blood vessels.

Xylem and phloem constitute the vascular bundle. Xylem distribute and store water. Phloem is responsible for transporting sugars, proteins, and other organic material. Similarly blood vessels in humans perform the function of delivering blood that contains gases, nutrients, waste, cells and hormones throughout the body.

From given information,

6]  the reason for line 2 of the proof: Given

7] the statement for line 4 of the proof:  BL ≅ LK  

8]  the reason for line 4 of the proof:  Definition of midpoint

9] the statement of line 5 of the proof: Δ BWL ≅ ΔKTL

10] the reason for line 5 of the proof: SAS postulate of triangle congruence

In this question, we have been given two triangles BWL and KTL.

We need to complete the proof.

A point L is the midpoint of line segment BK

Also, LW ≅ LT,

∠WLB ≅ ∠TLK

Consider,

             Statement                                         Reason

1)            LW ≅ LT                                             Given

2)        ∠WLB ≅ ∠TLK                                      Given

3)   L is the midpoint of BK                              Given

4)         BL ≅ LK                                           Definition of midpoint

5)       Δ BWL ≅ ΔKTL                      SAS postulate of triangle congruence

Therefore, from given information,

6]  the reason for line 2 of the proof: Given

7] the statement for line 4 of the proof:  BL ≅ LK  

8]  the reason for line 4 of the proof:  Definition of midpoint

9] the statement of line 5 of the proof: Δ BWL ≅ ΔKTL

10] the reason for line 5 of the proof: SAS postulate of triangle congruence

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