long division synthetic division

After solving an equation as per given relation of Lan, Lisa and Jim height ,now Lan's height is 174centimeters.

As given ,

Let h be Lan's height today in centimeters.

As per the relation between  Lan, Lisa and Jim height we have,

Lan=h cm

Lisa=h + 4

Jim=h -8

After 4 months, every month their heights increase by 2 cm

Lan=h + 8

Lisa=h + 4 +8

Jim=h -8 +8

Required equation for given condition:

Lan + Jim=170 +Lisa

⇒h +8 + h -8 + 8=170 + h + 4+8

⇒2h+8=h+182

⇒h=174cm

Therefore, after solving an equation as per given relation of Lan, Lisa and Jim height ,now Lan's height is 174centimeters.

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The coordinate of Point A is ([tex]\frac{1}{2} ,\frac{\sqrt{3} }{2}[/tex])

Given in the question;

From the figure,

To see the graph:

To find the coordinates of point A.

Now, According to the question and picture :

Point A is on the unit circle and

The angle between point A and the origin and

The X - axis is [tex]\frac{\pi }{3}[/tex] = 60°.

The radius of the unit circle is 1.

So, the x - coordinate of point A is :

X cos 60° = 1/2

The Y coordinate of point A is :

X sin 60° = [tex]\frac{\sqrt{3} }{2}[/tex]

Hence, The coordinate of Point A is ([tex]\frac{1}{2} ,\frac{\sqrt{3} }{2}[/tex]).

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A) ∠1 and ∠8 are alternate exterior angles

B) ∠4 and ∠6 are same side interior angles

E) ∠3 and ∠6 are alternate interior angles

Let's check the each options.

A) ∠1 and ∠8 are alternate exterior angles

The exterior angles are ∠1, ∠2, ∠7 and ∠8.

This is correct.

B) ∠4 and ∠6 are same side interior angles.

∠4 and ∠6 are inside the line m and n, they are in the same side, you can see it on the figure.

This is correct

C) ∠5 and ∠7 are vertical angles

∠5 and ∠7 are supplementary angles.

This is not correct.

D) ∠2 and ∠8 are  corresponding angles

These are same side of exterior angles.

This is not correct.

E) ∠3 and ∠6 are alternate interior angles

These are interior angles and alternative to each other.

This is correct.

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Answer:

6(3 + 4)

Step-by-step explanation:

GCF of 18 and 24 is 6

6 (3 + 4)

I hope this helps!

When Ken and Hamid race around a track, Ken completes a lap in 80 seconds while Hamid completes a lap in 60 seconds. ken will run 3 laps where as Hamid will run 4 laps.

Given that,

When Ken and Hamid race around a track, Ken completes a lap in 80 seconds while Hamid completes a lap in 60 seconds.

We have to find if they had faced off on the starting line, how many laps would they have won.

We have to find the LCM of the 80 and 60.

The prefix "LCM" stands for "Least Common Multiple." The smallest multiple that two or more numbers share is known as the least common multiple.

LCM of 80 and 60 is 240

240=80×3

ken will complete 3 laps.

240=60×4

Hamid will complete 4 laps.

Therefore, ken will complete 3 laps where as Hamid will complete 4 laps.

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Answer:

the answer is gonna be d

Step-by-step explanation:

Height was the tennis ball dropped if it bounces 42 inches is 0.7 inch.

What do you understand by direct proportionality?

If two quantities are directly proportional, it means that when one quantity increases at a certain rate, the other quantity also increases at the same rate up to a constant value. It is represented by the proportional symbol ∝.

Let the height of the ball bounces be h

The height of the ball drobbed from be y

It is given that the height that a ball bounces varies directly as the height from which it was dropped.

⇒ h ∝ y

⇒ h = ky where k is the constant of proportionality.

It is given that a tennis ball dropped from 14 inches.

⇒ y = 14 inches

Tennis ball bounces back to 8.4 inches.

⇒ h = 8.4 inches

⇒ 8.4 = k × 14

⇒ k = 8.4/14 = 0.6

Now, tennis ball dropped from 42 inches

y = 42

⇒ h = 42 × 0.6 = 0.7

Therefore, height was the tennis ball dropped if it bounces

42 inches is 0.7 inch.

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The required time at which the ball reaches a height of 10 ft is 0.5 sec.

Given that,
A ball is thrown into the air with an upward velocity o 12ft/s. The equation for the ball’s height (h) at any time (t) is h (t) =-4t^2+12t+5 find the time(s) at which the ball reaches a height of 10ft.

Here,
Given equation,
h(t) =-4t²+12t+5
For height 10 ft time,
10 = -4t² + 12t + 5
4t² - 12t + 5 = 0
4t² -10t - 2t + 5 = 0
2t(2t - 5) - 1(2t - 5) = 0
(2t-1)(2t -5) = 0
t = 1/2, 5/2  (5/2 can be negelected)

Thus, the required time at which the ball reaches a height of 10 ft is 0.5 sec.

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Answer:

y - 1 = - 3(x + 8)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 2 ← is in slope- intercept form

with slope m = - 3

• Parallel lines have equal slopes

the equation ofa line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - 3 and (a, b ) = (- 8, 1 ) , then

y - 1 = - 3( x - (- 8) ) , that is

y - 1 = - 3(x + 8)

Answer: Shirt = $7 and Sweater = $18

Step-by-step explanation:

5 Shirts, 3 sweaters = $89   (1)
9 Shirts, 8 sweaters = $207 (2)

1 Shirt = $?

1 Sweater = $?

Shirts = x

sweaters = y

(1) -> 5x + 3y = 89

(2) -> 9x + 8y = 207

(1) * 8 = 40x + 24y = $712

(2) * 3 = 27x + 24y = $621

(1) single out 24y -> 24y = $712 - 40x

put value of 24 y into (2)

(2) -> 27x + $712 - 40x = $621

Now solve

-13x = $-91

remove negative -> 13x = $91

x = $7

So a shirt is $7

And we can put $7 into (1) at the start -> 5(7) + 3(y) = $89

35 + 3y = $89

3y = $54

y = $18

Hence x = $7 and y = $18

So Shirt = $7 and Sweater = $18

Answer:

I don't see a table :/

Step-by-step explanation:

if a humming bird flaps his/her wings 500 times in 10 seconds you just have to do 500 x 6

humming birds flap their wings about 3000 times per minute

answer: 3,000

"Don't have a good day, have a great day"

-Guy

5 mph for 2 hours and 4 mph for 3 hours

4 mph for 2.25 hours and 6 mph for 1.5 hours

gives possible rates and times for two of his jogs

1.Let's determine the relationship between the rate of jogging and the time f jog in each scenario.

First Rate = [tex]\frac{6}{1.5} =4[/tex]  time = 1.5 hours

Second Rate =  [tex]\frac{5}{1.25} = 4[/tex] time = 1.5 hours

As a result, in this instance, the duration of his runs does not appear to be inversely related to their intensity.

2.First Rate = [tex]\frac{5}{2} =2.25[/tex]  time = 2 hours

Second Rate =  [tex]\frac{4}{3} =1.33[/tex] time = 3 hours

Therefore, in this instance, the duration of his runs appears to be inversely related to his pace.

3.First Rate = [tex]\frac{4}{2.25}[/tex]=1.77  time = 2.25 hours

Second Rate =  [tex]\frac{6.5}{1.5} =4[/tex] time = 1.5 hours

Therefore, in this instance, it appears that the duration of his runs is inversely related to his speed.

4.First Rate = [tex]\frac{4.5}{3}[/tex]=1.5  time = 3 hours

Second Rate =[tex]\frac{6}{4} =1.5[/tex]   time = 4 hours

Therefore, in this instance, it does not appear that the length of time he runs is inversely related to the speed at which he runs.

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Answer: 73015

Step-by-step explanation:

multiply both of them together

Answer:

86457

Step-by-step explanation:

The statement that cannot be assumed based on the figure is that

<DBC is vertical to <FDE. This makes option B the answer.

The given data consist of various intersections and line types however the line type used to vertical angles are not among.

The line type responsible for vertical angles or used for vertical angle theorem is the parallel lines and a transversal line. This two lines are used together to prove or get angles that are vertical

We can therefore conclude that <DBC is vertical to <FDE is the the correct option

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Answer:

Where's a photo or sum??

Using  Unitary Method  16 Oz for $2,24 ounces for $3 is a true statement.

As given in the question,

16 Oz for $2,24 ounces for $3 is solved by Unitary Method as follows:

16 Oz for $2

24 ounces for $3

Above statement is true.

If $2 fetches 16 Oz

then $1 will fetch 8 Oz

hence $3 will fetch 24 Oz (by Unitary Method)

Thus the given statement is true.

Alternately, the statement can be verified to be true or false as follows:

16 Oz for $2

1 Oz for $(2/16)

24 Oz for $ (24x2/16) = $3

Therefore, the given statement is valid and true. The Unitary Method has been applied either way to check the validity of the given statement and found to be valid (true). It is worthwhile to mention that Oz stands for ounces (abbreviation)

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If you just want to conduct a flyby and aren't planning to stay, it will take you approximately 600 days, and if you want to enter orbit, it will take you about 2,000 days.

Astronomical distances are expressed in terms of a light-year, which is also spelt light year. Its length is approximately 9.46 trillion kilometers, or 5.88 trillion miles.

NASA's Pioneer 10 was the first spacecraft to ever travel across the distance between the Earth and Jupiter. On March 3, 1972, it was launched, and on December 3, 1973, it arrived. There were 640 days of flight time altogether.

However, Pioneer 10 was passing by while en route to study the outer solar system. Before NASA lost communication with it, the spacecraft traveled another 11 years into deep space after approaching the planet at a distance of 130,000 kilometers, where it snapped the first-ever close-up images of Jupiter.

Pioneer 11 launched and touched down one year later. It traveled there in 606 days, flying by Jupiter at a considerably closer distance (21,000 kilometers), and also stopped by Saturn.

The Voyager spacecraft arrived next. Voyager 1 arrived on March 5, 1979, in only 546 days, and Voyager 2 took 688 days.

Consequently, it will take between 550 and 650 days to complete a flyby.

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Step-by-step explanation:

students who like both festivals

140+150=290

290-260=30

=30

students who like one festival

260-150=110

=110

Answer:

118.558 cm^2

Step-by-step explanation:

Ok, a rectangular cube and a Cylinder.

Let's start with the rectangular cube.

SA= 2(lw + lh + wh)

total surface area = 94 cm^2

Now the Surface Area of the of the Cone.

A=2πrh+2πr^2

A=2πrh+2πr^2=2·π·1·5+2·π·1^2≈37.69911 cm^2

Since the cone is standing on top of the rectangular cube, we need to deduct just the area of the circle.

A=πr2=π·12≈3.14159 cm^2

So, 84 cm^2 + 37.69911 cm^2 - 3.14159 cm^2

Sum the quantities:

84 cm^2 + 37.6991 cm^2 - 3.14159 cm^2

Sum the numbers 84 + 37.7 - 3.142 = 118.558:

Answer: 118.558 cm^2

According to the solving the following equation:

The standard form: x³ + 3x² - 6x - 8

degree: 3

constant term: 8

A polynomial is a mathematical equation made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division operations.

No part of an algebraic expression should be - Variables' square roots. variable powers that are fractional. variable powers that are negative. variables in any fraction's denominator.

Given polynomial, (x + 4) (x - 2) (x + 1)

Keeping the third bracket constant while simplifying the first two results in,

= (x² - 2x + 4x - 8)(x +1 )

= (x² + 2x - 8)(x+1)

On further simplifying we get,

= x³ + 2x² +x² -8x +2x -8

= x³ + 3x² - 6x - 8

So, the standard form is x³ + 3x² - 6x - 8  , degree is 3, leading co-efficient is 1 and the constant term is -8

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The segments are parallel to TU and WX

So, The correct options are 2 and 3

Given,

The slope of MN is -3

To find the which segments are parallel to MN?

Now, According to the given options:

We know that,

The slope of parallel lines are always equal. Therefore the line which have slope -3 is parallel to MN.

The formula to find the slope is:

m = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

Now, Slope for PQ,

[tex]m_{1} = \frac{7-6}{8-3}[/tex]    = 1/5

Slope for TU,

[tex]m_{2} = \frac{10-1}{5-8} =[/tex] -3

Slope for WX,

[tex]m_{3} = \frac{0-6}{4-2} = \frac{-6}{2} =[/tex] -3

Slope for RS,

[tex]m_{4} = \frac{2-3}{4-1} =[/tex] -1/3

Therefore, The segments are parallel to TU and WX

So, The correct options are 2 and 3

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The coordinates of Hector's friend's house are (18,3).

Given:

Coordinates of Hector's house = (-7,11)

Coordinates of zoo = (-7,3)

He walked a total distance of 25 blocks from the zoo towards the east.

This means that he walked horizontally on the y-axis to reach his friend's house. So, the y-coordinate remains 3 and only the x-coordinate varies.

To find the coordinates of Hector's friend's house,

As given each unit on the map represents one block.

25 units = 25 blocks

Adding 25 units to the x- coordinate of the zoo keeping the y-coordinate same to obtain the required coordinates.

- 7 + 25 = 18

Therefore, the coordinates of Hector's friend's house are (18,3).

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x-intercept, 7/2

y-intercept, -7/3

The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively. the location on the y axis where a graph crosses it. • x = 0 at the same location. An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.

Given that,

The graph of the equation 2x-3y=7 is a line.

2x-3y=7

Divide 7 on both sides

2x/7- 3y/7=1

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

x-intercept, 7/2

y-intercept, -7/3

Therefore, x-intercept, 7/2, y-intercept, -7/3.

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Answer and Explanation:

Let x be the total weight of the silver alloy costing $3.50 per ounce and y be the the total weight of the other that costs $7.00 per ounce.

The total weight of the resulting alloy is 30 ounces.

x+y=30x+y=30

Each ounce of the mixture must cost $6.30. The total cost of the resulting silver alloy is:

https://homework.study.com/explanation/a-jeweler-wants-to-make-a-silver-alloy-to-be-used-to-make-necklaces-how-many-ounces-of-a-silver-alloy-that-costs-3-50-per-ounce-should-be-mixed-with-one-that-costs-7-00-per-ounce-to-make-a-new-30-ounce-alloy-that-costs-6-30-per-ounce.html

8 ounces of silver alloy that costs $5.50 per ounce should be mixed with 12 ounces of silver alloy that costs $8.00 per ounce to make a new 20-ounce alloy that costs $7.00 per ounce.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Let x be the number of ounces of silver alloy which costs $5.50 per ounce and y be the number of ounces of silver alloy that costs $8.00 per ounce.

We have,

x + y = 20

5.50x + 8.00y = 7 × 20

From the first equation, x = 20 - y

Substituting this in the second equation,

5.5 (20 - y) + 8y = 140

(5.5 × 20) - 5.5y + 8y = 140

110 + 2.5y = 140

2.5y = 30

y = 12

x = 20 - y = 20 - 12 = 8

Hence the number of $5.50 cost per ounce silver alloy used is 8 ounces and the other alloy used is 12 ounces.

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a) A circle graph inaccurately displays the data because the data is not about parts of a whole.

b) Line graph would best display the data.

A circle is divided into sectors that each represent a component of a whole to create a circle graph, which is a visual representation of data.

An individual data point is connected by a line in a line graph, sometimes referred to as a line plot or a line chart. A line graph shows numerical values over a predetermined period of time.

a) Since circle graphs are designed to depict data consisting of parts of a whole, a data set consisting of temperature variations over the course of a week would be wrongly displayed by one.

b) Since line graphs are the most appropriate for a data set that is tied to time, a line graph would be the most effective way to display the given data.

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We need to know about trigonometry to solve this problem. The measure of angle G is 27.9°

Trigonometry is related to functions of angles and their applications. There are six main functions of an angle, sine, cosine, secant,cosecant,tangent and cotangent. Here in this question we know the measure of all the sides of the triangle, and the angle T is 90°. We will be using the function tangent(tan) to solve for angle G. The base of the triangle is RG and the height is TR.

RG=8  TR=15

tan G=base/height=RG/TR=8/15=0.533

G=[tex]tan^{-1}[/tex] 0.53=27.9°

Therefore the measure of the angle G is 27.9°.

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