alegbra 2: pls help!!

Kiara and Sean are setting off model rockets. Kiara's rocket's flight pattern can be modeled by the function f(t)= -16t² +80t. Sean's rocket's flight
pattern can be modeled by the function h(t) = -16t² + 120t+64. In each function, t is the time in seconds after the rockets launch and f(t) and h(t)
are the heights of the rockets in feet.
How many seconds after Kiara's rocket returns to the ground does
Sean's rocket return to the ground?
Enter your response as a numeric answer. Do not include spaces, units,
or commas in your response.

Answers

Answer 1

Answer:

Sean's rocket lands 3 seconds after Kiara's rocket.

Step-by-step explanation:

Kiara:  f(t)= -16t² + 80t

Sean:  h(t) = -16t² + 120t + 64

Assume that both rockets launch at the same time.  We need to be suspicious of Sean's rocket launch.  His equation for height has "+64" at the end, whereas Kiara's has no such term.  The +64 is the starting height iof Sean's rocket.  So Kiara has a 64 foot disadvantage from the start.  But if it is a race to the ground, then the 64 feet may be a disadvantage.  [Turn the rocket upside down, in that case.  :) ]

We want the time, t, at which f(t) and h(t) are both equal to 0 (ground).  So we can set both equation to 0 and calculate t:

Kiara:  f(t)= -16t² + 80t

0 = -16t² + 80t

Use the quadratic equation or solve by factoring.  I'll factor:

0 = -16t(t - 5)

T can either be 0 or 5

We'll choose 5.  Kiara's rocket lands in 5 seconds.

Sean:  h(t) = -16t² + 120t + 64

0= -16t² + 120t + 64

We can also factor this equation (or solve with the quadratic equation):

0 = -8(t-8)(2t+1)

T can be 8 or -(1/2) seconds. We'll use 8 seconds.  Sean's rocket lands in 8 seconds.

Sean's rocket lands 3 seconds after Kiara's rocket.


Related Questions

Select the correct answer.
Graph the following system of inequalities.
y ≥x-2
y ≤-4x - 2
y
-6-5
6
0 1 2 3 4
X
9
5
2
F
6
12 RE
NUE
F
4 5 6

Answers

Answer:

I don't understand the formatting after the first two equations.

Step-by-step explanation:

See attached graph.

PLEASE HELP ASAP, I WILL GIVE 40 POINTS IF THE RIGHT ANSWER, AND BRAINLEST, ASAP

Answers

Answer:

8 types of sandwiches.

Step-by-step explanation:

she has choices of :

1 turkey sandwich

1 roast beef sandwich

1 ham sandwich

1 white sandwich

1 white bread sandwich

1 American sandwich

1 swiss sandwich

1 colby cheese sandwich.

Answer:

8 types

Step-by-step explanation:

she had alot of choice like :

Turkey, roast beef, ham, swiss, corby cheese, wheat or whitebread and american sandwhich .

A figure has vertices at A(—3, 2), B(—l, —l), and C(—4, —2). After a transformation,the image of the figure has vertices at A'(3, 2), B'(l, —l), and C'(4, —2). Draw the preimage and image. Then identify the transformation

Answers

Answer:

rotate 180° about origin

The preimage and image of the figure are given below. The transformation rule that is applied is (x, y) → (-x, y).

Given a triangle with vertices A(—3, 2), B(—l, —l), and C(—4, —2), which is preimage. Further, an image is created of this triangle that has vertices at A'(3, 2), B'(l, —l), and C'(4, —2). As shown in the given figure.

Now, as per the image and preimage in the given graph. The image is the reflection of the preimage about the y-axis. This can be verified as when the image and preimage are reflected about the y-axis the vertices change as:

(x, y) → (-x, y)

A(-3, 2) → A'(3,2)

B(-1, -1) → B'(1, -1)

C(-4, -2) → C'(4,-2)

Hence, the transformation rule is (x, y) → (-x, y).

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Quick algebra 1 question for 10 points!

Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!

Answers

Answer:

[tex]f(x)=-2(x-3)^2+2[/tex]

Step-by-step explanation:

To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute 0 for x and solve for y.

x-intercept(s): (2,0),(4,0)

y-intercept(s): (0,−16)

Answer:

D     f(x) = -2(x - 3)² + 2

Step-by-step explanation:

The y-intercept occurs at x = 0.

A

f(x) = 2x(x + 14) - 64

f(0) = -64     Not -16

B

f(x) = (x + 4)² + 2x

f(0) = 16     Not -16

C

f(x) = (x - 16)² + 4

f(0) = 260      Not -16

D

f(x) = -2(x - 3)² + 2

f(0) = -18 + 2 = -16   <-------------------- this is it

Each sales associate at an electronics store has a choice of the two salary options shown below:

$115 per week plus 9.5% commission on the associate’s total sales

$450 per week with no commission


The average of the total sales amount for each associate last year was $125,000. Based on this average, what is the difference between the two salary options each year? (1 year = 52 weeks)

Answers

Using proportions, it is found that the difference between the two salary options each year is of $5,545.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

For the first option, $115 per week plus 9.5% commission on the associate’s total sales, the yearly salary is:

115 x 52 + 0.095 x 125000 = $17,855.

For the second option, $450 per week with no commission, the yearly salary is:

450 x 52 = $23,400.

Hence the difference is given as follows:

23400 - 17855 = $5,545.

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4|a|+8-a if a=-2

ASAP GIVING BRAINLIEST PLEASE HELP!!

Answers

Answer: 18

Step-by-step explanation:

4 I-2I + (8+2)=

4(2) + 8+2=

8+8+2=

18

At noon, ship a is 40 nautical miles due west of ship b. ship a is sailing west at 18 knots and ship b is sailing north at 17 knots. how fast (in knots) is the distance between the ships changing at 5 pm? (note: 1 knot is a speed of 1 nautical mile per hour.)

Answers

The distance between the ships changing at 92.29 Knots

Using the position of ship A as the reference point, at time t measured in hours past noon, ship A is 18 t miles west of this point and ship B is 40 + 17t north of this point. The distance between ships is then

                              [tex]d(t) = \sqrt{(18t)^{2} + (40+17t)^{2} } \\[/tex]

The rate of change of distance is -

                              [tex]\frac{dd}{dt} = \frac{36t + 2(40 + 17t)17}{2\sqrt{18t^{2} + (40 + 17t) } }[/tex]

after putting t = 5 into this rate of change ,

we get, answer = 92.29

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help please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111

Answers

Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Given solution of a question done by two people.

Jenna's method

5(30+4)

(5)(30)+(5)(4)

150+20=170

Mia's method

5(30+4)

5(34)=170

We are required to find why they have achieved at the same answer.

Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.

Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

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Refer to the figure to the right.
A. If RV RT, name two congruent angles.
B. If RSSV, name two congruent angles.
C. If LSRT LSTR, name two congruent segments.
D. If LSTV= LSVT, name two congruent segments.
R
T

Answers

Answer:

c if lsrt lstr name two congruent segments

Samantha and mia each left julia’s house at the same time. mia walked north at 7 kilometers per hour. samantha ran west at 11 kilometers per hour. how far apart were they after one hour? round the answer to the nearest tenth. a right triangle. a point at the angle with measure 90 degrees is labeled julia's house. a line drawn north is labeled 7 kilometers and a line drawn west is labeled 11 kilometers.

Answers

Samantha and Mia are 13 km apart from each other.

What is Pythagorean ?

A right triangle's squared sides add up to the hypotenuse's squared length, according to the Pythagorean Theorem.

Mia is 7 kilometers north of Julia's home as she walked at a speed of 7 kilometers per hour.

Samantha walked at an average speed of 11 km/h, and she is now 11 kilometers west of Julia's home.

A right-angled triangle is formed by Julia's house, Mia and Samantha's locations after one hour, and the figure's points.

Hypotenuse of the triangle, which measures distance between the females

the Pythagorean theorem,

H² = P² + B²

H² = 7² + 11²

H² = 49 + 121

H = √170

H = 13.038

H = 13km

Between them, there is a 13 kilometer distance.

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perimeter of a quadrilateral is 590m its sides are in ratio 5 ratio 12 ratio 17 ratio 25 find the area of the quadrilateral​

Answers

Answer:

255,000,000m^2

Step-by-step explanation:

Let 5:12:17:25 be 5x, 12x, 17 x, 25x respectively

So

Perimeter of quadrilateral=5x+12x+17x+25x

590m=59x

590m/59=x

10m=x

So now value

5x= 5*10 =50

12x= 12*10 =120

17x= 17*10 =170

25x= 25*10 =250

Now

Area of quadrilateral=50m*120m* 170m* 250m

=255,000,000m^2

Step-by-step explanation:

if I understand you correctly the sides are in a

5 : 12 : 17 : 25 ratio.

a ratio is basically a fraction. but instead of the denominator telling us the structure of the whole (e.g. 2/5 tells us that the whole is split into 5 equal parts), a ratio tells us this by the sum of its elements :

5 : 12 : 17 : 25

means that the whole perimeter of the quadrilateral has

5 + 12 + 17 + 25 = 59 equal parts.

since the perimeter is 590 m, we know with 59 equal parts, that one part is 590/59 = 10 m.

so, the sides are

50 m, 120 m, 170 m, 250 m

but for the area of the quadrilateral there is at least the information of one angle missing.

to have just the 4 side lengths is not enough. these sides can still have all kinds of angles between them, which creates different areas.

rounding to 1 significant figure, estimate the
answers to these questions:
a)
78 × 92
b)
615 × 38
C)
423 × 764

Answers

Answer:

a) 7000

b) 20000

c) 300000

Rounding is the act of replacing a number with values that are an approximation.

can be used to create simpler, or more explicit answers

Basic rounding rules:

1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 68 rounded to 1 significant figure would be 70.

2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 13 rounded to 1 significant fugue is 10.

3. Zero digits that come after a non zero digit are non significant. Example: 10000 only has 1 significant figure

Calculations:

A) 78 x 92 = 7176

to round to 1 sig fig we must make all digits after 7 insignificantwe must also take note of whether the 7 will remain the same or be rounded upthe digit that comes after is a 1, following the rules of rounding it will remain a 7

The answer for A is 7000

B) 615 x 38 = 23370

all digits after 2 must be insignificant the digit that comes after is a 3,  following the rules of rounding the 2 will remain a 2

Answer for B is 20000

C) 423 x 764 = 323172

all digits after 3 must be insignificantthe digit that comes after is a 2, following the rules of rounding the 3 will remain a 3

Answer for C is 300000

how many rectangles of different sizes can be formed from 36 identical rectangles

Answers

Answer:

i think answer is 5

Step-by-step explanation:

since you could think what are factors of 36
1x36
2x18
3x12
4x9 and
6x6

If a system reliability of 0. 998 is required, what reliability of two components in series is required?

Answers

The reliability of two components in series is 0.996.

To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.

Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.

We can find this probability multiplying all the ten reliabilities:

P = 0.998^2 = 0.996004

Rounding to three decimal places, we have P = 0.996

The reliability of the engine is 0.996.

Hence,

The reliability of two components in series is 0.996.

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Find the area of the shaded region. Round the answer to the nearest
tenth decimal place.

Answers

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Area of shaded region = 2571.66 in²

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Radius of smaller circle = 25 in

Radius of larger circle = 25 + 13 = 38 in

Area of ring : Area of larger circle - Area of smaller circle

[tex]\qquad❖ \: \sf \:\pi {(38)}^{2} - \pi {(25)}^{2} [/tex]

[tex]\qquad❖ \: \sf \:\pi( {38}^{2} - 25 {}^{2} )[/tex]

[tex]\qquad❖ \: \sf \:3.14(1444 - 625)[/tex]

[tex]\qquad❖ \: \sf \:3.14(819)[/tex]

[tex]\qquad❖ \: \sf \:2571.66 \: \: in {}^{2} [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Area = 2571.66 in²

please help! look at the phot linked

Answers

Answer:  C

Step-by-step explanation: the other two options are both wrong, 0.13 is larger than 0.125 and she did order by volume per fish.

Help!!!!
A system of inequalities is shown.
Which system Is represented in the graph?

Answers

The system of inequalities represented on the graph is:

y > 2x + 3.y > (x + 1)² - 4.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The linear function in this problem has y-intercept of b = 3, and also goes through the point (1,5), hence the slope is of 2. The line is dashed, hence it is not included in the solution, hence only the part greater than the line is, hence:

y > 2x + 3

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this graph, the vertex of the parabola is of (-1,-4), hence h = -1, k = -4, and the equation is:

y = a(x + 1)² - 4

When x = 0, y = -3, hence the leading coefficient is found as follows:

-3 = a - 4

a = 1.

Hence:

y = (x + 1)² - 4.

And the inequality is:

y > (x + 1)² - 4.

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find the perimeter of the figure below, composed of a rectangle and two semicircles
.​

Answers

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's consider the shape given to us:

 ⇒ a rectangle with two semicircles cutout on the edges

     ⇒ perimeter/circumference of the two semicircles can count as one

         circle

         

Let's solve:

 Circumference = circumference of two semicircle

               [tex]\hookrightarrow \text{Total circumference} =\frac{1}{2} *\pi *\text{ diameter} +\frac{1}{2} *\pi * \text{diameter}\\= \pi *\text{diameter}=10\pi =10 * 3.14 = 31.4[/tex]

Total Perimeter = 31.4 + 14 + 14 = 31.4 + 28 = 59.4

Answer: 59.4 square units

Hope that helps!

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Dean's father, Franco, is 5 times his age. Dean is 8 years older than his sister, Helen. The sum of their ages is 62 years. How old is each person

Answers

Answer:

dean = 10

franco = 50

helen = 2

steps

you want to get the age of one of the people first

'is' means equal

'older than' means plus

'sum' means total by adding

d

f = 5d

d = 8 + h

d + f + h = 62

make sure there is 1 letter to solve for

d = 8 + h -> h = d - 8

f = 5d

d = d

d + f + h = 62

d + (5d) + (d-8)

7d - 8 = 62

7d = 70

d = 10

f = 50

h = 2

Find the equation of a line that is perpendicular to line g that contains (p, q). coordinate plane with line g that passes through the points negative 2 comma 6 and negative 3 comma 2 4x y = q 4p x − 4y = −4q p −4x y = q − 4p x 4y = 4q p

Answers

The equation of a line that exists perpendicular to line g contains (P, Q) exists x + 4y = 4Q + P.

How to estimate the equation of the line that exists perpendicular to line g that contains (p, q) coordinate plane with line g?

Given: Coordinate plane with line g that passes through the points (-2,6) and (-3,2).

The coordinate of G: (-2,6) and (-3,2)

Let, [tex]$&\left(x_{1}, y_{1}\right)=(-2,6) \\[/tex] and [tex]$&\left(x_{2}, y_{2}\right)=(-3,2)[/tex]

The slope of a line [tex]$\mathbf{g}$[/tex] :

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

[tex]$m &=\frac{2-6}{-3-(-2)} \\[/tex]

[tex]$m &=\frac{-4}{-1} \\[/tex]

m = 4

So, the slope of a line g exists 4.

To find the slope of a line perpendicular to g,

[tex]$&m_{1}=-\frac{1}{m} \\[/tex]

[tex]$&m_{1}=-\frac{1}{4}[/tex]

The equation of the slope point form of the line exists

[tex]$\left(y-y_{1}\right)=m\left(x-x_{1}\right)$[/tex]

[tex]$y-Q=-\frac{1}{4}(x-P)$[/tex]

[tex]$4 y-4 Q=-x+P$[/tex]

[tex]$x+4 y=4 Q+P$[/tex]

Therefore, the equation of a line that exists perpendicular to line g contains (P, Q) exists x + 4y = 4Q + P.

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Towns A, B, and C lie on a straight line, as shown below. Jack and Arthur start at Town B and drive for an hour from Town B to Town C, where they stop for an hour to eat lunch. Which of the following graphs could represent their distance from Town A during these two hours?

Answers

The situation described by the distance from Town A is the first graph.

Given that cities A,B and C are on straight line.

We are required to find the graph appropriate the given situation.

Distance is basically the measurement of how far two things,places are located.It can be measurement from one point to another .

On the first hour,they leave town B to town C moving farther from Town A,hence the distance is increasing on the first hour.

On the second hour they stop for lunch,meaning that the distance remains constant at the point, it was at the end of the first hour.

Hence if towns A,B C lie on a straight line and Jack and Arthur start at town B and drive for an hour from Town B to Town C then the distance shown from Town A during these two hours is first graph.

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The probability distribution histogram shows the age distribution of giraffes at a zoo.

What is P(4


Enter your answer, as a decimal, in the box.

Answers

The value of P(4<X≤12) is 0.45

How to determine the probability?

The complete question is added as an attachment

To calculate P(4<X≤12), we use the following equation

P(4<X≤12) = P(4<X≤8) + P(8<X≤12)

From the histogram, we have:

P(4<X≤8) = 0.1

P(8<X≤12) = 0.35

So, we have:

P(4<X≤12) = 0.1 + 0.35

Evaluate

P(4<X≤12) = 0.45

Hence, the value of P(4<X≤12) is 0.45

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What is the solution to this system of equations?

4x + 5y = 7

3x – 2y = –12



The solution is

Answers

The solution to the system of equations is (-2, 3)

A scientist uses a submarine to study ocean life.
She begins 86 feet below sea level.
After traveling down for 3 seconds, she's 193 feet below sea level.

Find the rate of change in the submarine's elevation in feet per second. Round your answer to the nearest tenth.

Answers

Answer: 35.7 feet per second.

Step-by-step explanation: The scientist starts at -86 feet. Then she goes to -193 feet. The difference here is 193-86 =  107 feet. That means she traveled 107 ft in 3 seconds. 107/3 = 35 with a remainder of 2. 2/3 approximately equals 0.6666667. We need to round to the nearest tenth which is 0.7. So, we are left with  35.7.

Choose the numbers that are terminating decimals. Select all that apply.
A. 0.032
B. 0.999...
C. 0.525
D. 0.75

Answers

Answer: A, C, and D

Step-by-step explanation:

          A terminating decimal is a decimal that has an end. In other words, [tex]\frac{1}{4} =0.25[/tex] is one, but [tex]\frac{1}{3} =0.3333...[/tex] is not.

✓ A. 0.032

✗ B. 0.999...

✓ C. 0.525

✓ D. 0.75

You are interested in doing a content analysis on the characteristics people seek in a partner by examining the personals section of three newspapers. your unit of analysis is:_______.

Answers

To do content analysis on the characteristics people seek in a partner by examining the personals section of three newspapers the unit of analysis will be objective of the section.

Given that we are interested in doing content analysis on the characteristis people seek in a partner by examining the personals section of three newspaper.

Content analysis is basically a research tool used to determine the presence of certain words, themes,or concepts within some given qualitative data. Using content analysis, a researchers can quantify and analye the presence meanings and relationships of such certain words, themes and concepts.

When we are required to do content analysis by examining the personals section of three newspapers, its units can be objective of section. Some part is related to matrimonials, some are for rent,etc.and some are for commercial advertisements.

Hence the unit of analysis is objective of the section.

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(01.02 mc)matt is showing his work in simplifying (6.2 − 1.6) − 4.4 7.8. identify any error in his work or reasoning. step 1: (6.2 − 1.6) − 4.4 7.8 step 2: 6.2 (− 1.6 − 4.4) 7.8 (commutative property) step 3: 6.2 − 6 7.8 step 4: −14 − 6 = 8 (commutative property) step 5: 14 − 6 = 8 he wrote commutative instead of distributive in step 4. he wrote commutative instead of distributive in step 2. he wrote commutative instead of associative in step 4. he wrote commutative instead of associative in step 2.

Answers

The correct option is (d)

He wrote commutative instead of associative in step 2.

What is the commutative property?

According to the commutative property, a mathematical principle, the product of a multiplication does not depend on the order in which the numbers are multiplied.

Commutative property:  a+b = b+a

Associative property: (a+b) + = a+(b+c)

Now consider the provided expression.

(6.2 − 1.6) − 4.4 + 7.8

Step 1:

(6.2 − 1.6) − 4.4 + 7.8

Step 2 Use Associative property

6.2 + (−1.6 − 4.4) + 7.8

Step 3: Simplify

6.2 − 6 + 7.8

Step 4: Use commutative property

14 − 6

Step 5: Simplify

14 − 6 = 8

Hence, the wrong step is step 2.

He wrote commutative instead of associative in Step 2.

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I understand that the question you are looking for is:

Matt is showing his work in simplifying (6.2 − 1.6) − 4.4 + 7.8. Identify any error in his work or reasoning. Step 1: (6.2 − 1.6) − 4.4 + 7.8 Step 2: 6.2 + (− 1.6 − 4.4) + 7.8 (commutative property) Step 3: 6.2 − 6 + 7.8 Step 4: −14 − 6 = 8 (commutative property) Step 5: 14 − 6 = 8

(a)-He wrote commutative instead of distributive in Step 4.

(b)-He wrote commutative instead of distributive in Step 2.

(c)-He wrote commutative instead of associative in Step 4.

(d)-He wrote commutative instead of associative in Step 2.

A student is trying to solve the system of two equations given below: equation p: y z = 6 equation q: 8y 7z = 1 which of these is a possible step used in eliminating the y-term? (y z = 6) ⋅ −8 (y z = 6) ⋅ 7 (8y 7z = 1) ⋅ 7 (8y 7z = 1) ⋅ 8

Answers

Correct option for solving the system of two equation is ([tex]y\times z =6[/tex])[tex]\times -8[/tex] .

What is simultaneous linear equation?

A system of simultaneous linear equations is any set of two or more linear equations that share the same unknown variables. Finding values for the unknown variables that simultaneously satisfy all of the equations is required to solve such a system.

Simultaneous linear equations are two linear equations in two variables put together.

The ordered pair (x, y) that satisfies both linear equations is the system of simultaneous linear equations' solution.

Given,

Equation p: [tex]y+z=6[/tex]

Equation q: [tex]8y+7z=1[/tex]

To solve the above simultaneous linear equation multiply the equation p with (-8)

[tex](y+z=6)\times -8[/tex]     ...................................................... Equation (1)

Now add Equation (1) with Equation (q)

[tex]-8y-8z=-48[/tex]

+ [tex]8y+7z=1[/tex]

⇒ [tex]-z=-47[/tex]

⇒ [tex]z=47[/tex]

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PLS HELP ASAP! THX

Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
Find (h-g)(2.1)

Answers

The value of the polynomial difference when the value of x is 2.1 is -3.51

Difference of polynomials

Polynomials are functions that has a leading degree of 3 and above. Given the following polynomial expression below;

g(x)= 2x^2+3x-9 and;

h(x)=x^2+2x-6

Take the difference

(h-g)(x) = h(x) - g(x)

Substitute

(h-g)(x) = x^2+2x-6 - (2x^2+3x-9)

(h-g)(x) = x^2+2x-6-2x^2-3x+9
(h-g)(x) = -x^2-x+3

Substitute the value of x to have;

(h-g)(2.1) = -(2.1)^2 - 2.1 + 3

(h-g)(2.1) = -4.41 + 0.9

(h-g)(2.1) = -3.51

Hence the value of the polynomial difference when the value of x is 2.1 is -3.51

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The perimeter of a rectangle is 320 feet. Find the length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.

Answers

The length is 25 feet and the width is 135 feet

What are consecutive odd integers?

Consecutive odd integers differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers.

How to find the perimeter of the rectangle?

⇒Perimeter of rectangle = 2(l+w)

The perimeter of a rectangle is 320 feet

let the length of a rectangle is x

The next consecutive odd integer is x+2

width = 5(x+2)

=5x+10

2(length + width) = 320

l+w=160

x+5x+10=160

6x=150

x=25

length = 25 feet

width = 5(25+2)=135 feet

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