Subtract the following polynomials

1. (q² + 8) - (4q² + 1)

2. (3x + 7x² - 6) - (5x² + x + 9)​

Answer:

1.) The slope is 2

2.) The y-intercept is (0,1)

3.) y = 2x + 1

Step-by-step explanation:

1.) you can either use rise over run or the slope formula. rise over run is quicker, but here's the formula:

you can use any two points on the line, i chose (2, 5) and (1, 3)

[tex]\frac{(y_{2}-y_{1})}{(x_{2}-x_{1})} \\[/tex]

[tex]\frac{3-5}{1-2} \\\\\frac{-2}{-1} \\\\\frac{2}{1} \\\\2[/tex]

2.) for the y-intercept, you just look for the point where the graph crosses the y-axis and x = 0

3.) using the formula y = mx + b, m being the slope and b being the y-intercept, you take the information above and plug it in to get y = 2x + 1

i hope this helped!

Answer:

y=-2x+3

Step-by-step explanation:

Use the slope formula

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

According to the table, x=1 and y=1. There is another point x=2 and y=-1.

We can say that [tex]x_{1}=1[/tex] and [tex]y_{1} =1[/tex]. We can also say that [tex]x_{2}=2[/tex] and [tex]y_{2}=-1[/tex]. Plugging this into the equation we get:

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

This means that the slope of your equation is -1/2

Point intercept form is y=mx+b

So plugging the slope in we have [tex]y=2x+b[/tex]

We can plug in one of the values from the value table for x and y, but to keep things simple, I’m going to just use x=1, and y=1, the first values on the table. Plugging these into the equation we get:

[tex]1=-2(1)+b\\ 1=-2 +b\\b=1+2 \\b=3[/tex]

So our equation is [tex]y=-2x+3[/tex]

Answer:

1/3 = slope

Step-by-step explanation:

Start with

y = mx + b    

                  b = -5 given ,  now sub in the given point to calculate m =slope

-4 = m(3) - 5      add 5 to both sides

1 = m(3)               divide through by 3

1/3 = m = slope

The value of w from the given equation is w=(x-3y+1)/3.

Given  an equation x=3(y+w)-1 and we have to find the value of w in terms of x and y.

Equation is relationship between two or more variables expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation.

The given expression is x=3(y+w)-1 and we have to find the value of w. To find the value we have to first solve the right side of the equation.

x=3y+3w-1

Now take w at one end and all other variables in other end.

3w=x-3y+1

Now divide both sides by 3.

3w/3=(x-3y+1)/3

Now cancel 3 from numerator and denominator in left side.

w=(x-3y+1)/3

Hence the value of w in the equation x=3(y+w)-1 is w=(x-3y+1)/3.

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Answer:

Step-by-step explanation:

Answer: 17 campers attended last year

Step-by-step explanation:

Let x be the number that attended last year.

The number of campers this year (23) is equal to 2 times the number of last year (x), minus 11.

23 = 2x – 11

23 + 11 = 2x

34 = 2x

34/2 = x

17 = x

Using variable concepts, of dependent and independent variables, it is found that the dependent variable is the amount of sales dollars earned.

In this problem, the manager believes that the amount of sales dollars earned is a function of the number of contacts that the salesperson makes, hence:

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44% is the answer

6 Article price at buying =5 Rs

1 Article price at buying = 5/6...(i)

5 Articles sold at Rs. 6

1 Articles cost at sold = 6/5 ....(ii)

% Gain=((6/5 - 5/6)/ 5/6) * 100

= 11/25 * 100 = 44%

Profit is a general increase in an asset or the value of an asset. If the item's current price is higher than the original purchase price, you will make a profit. For accounting and tax purposes, profits can be categorized in several ways: B. Gross profit and net profit, or realized profit and unrealized (paper) profit.

The definition of victory is profit, benefit, or increase. An example of profit is a 5% increase in income over the past year. An example of a win is a 5 point lead over another team.

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The total number of light bulbs the company will make in weeks 9.36 × 10² is 4.27 × [tex]10^{6}[/tex] bulbs.

Work completed in a certain length of time is referred to as productivity (power). One hour, one minute, or one second makes to a unit.

Calculation for the total number of bulbs produced in given week;

Number of bulbs produced per week = 4.56 × 10³

Now, estimate how many bulbs will be produced in 9.36 × 10² weeks.

To estimate how many light bulbs were created in the allotted period, we will simply multiply both values.

Number of light bulbs the company will make in 9.36 × 10² weeks is;

= 4.56 × 10³ × 9.36 × 10²

= 4.27 × [tex]10^{6}[/tex]

Therefore, the total number of bulbs produced in weeks 9.36 × 10² is 4.27 × [tex]10^{6}[/tex] bulbs.

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The complete question is -

A company produces 4.56*10^3 light bulbs each week. Written in scientific notation, which is the best estimate of how many light bulbs the company will make in 9.36*10^2 weeks?

Option a is correct.

What is dimension analysis?

Dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities and units of measure and tracking these dimensions as calculations or comparisons are performed.

We can convert qt/min to gal/h as shown below:

1 qt = 0.25 gallon

1 min = 1/60 hour

4.5 qt/min = (4.5*0.25)/ (1/60) gal/h

= 4.5*0.25*60 gal/h

= 67.5 gal/h

Hence option a is correct.

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Using the Pythagorean Theorem, the perimeter of the triangle is of 58.7 cm.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

From your description, I will suppose that the legs are of 6 cm and 26 cm, hence the hypotenuse is:

[tex]h^2 = 6^2 + 26^2[/tex]

[tex]h = \sqrt{6^2 + 26^2}[/tex]

h = 26.7.

The perimeter is the sum of the lengths of the three sides, hence:

P = 26.7 + 26 + 6 = 58.7 cm.

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Answer:

The probability of the frog landing on a complement of yellow lily is 0.57

Step-by-step explanation:

PLANTS Of the water lilies in the pond, 43% are yellow. The others are white.

It is given that 43% of plants are lilies it means the probability of a frog randomly jumping onto a lily is:

the probability of the frog landing on a complement of yellow lily is 0.57

Step-by-step explanation:

the functional graph is the line.

a functional graph is always showing the direct relationship between a value on one coordinate axis with a value in the other coordinate axis

here it is between the price in dollars (as we can understand it : per unit) and the number of units sold.

clearly, the more units we sell, the cheaper we have to make the price per unit.

the question is how many units can be sold for a given price ($60).

so, I find the given price on the price axis (in this case the vertical axis), go then along that price all the way to the right until I hit the function line, and then go straight down to the unit axis and see what value I am hitting there : 80. which means 80,000 units.

so, I can sell 80,000 units for $60 per unit.

The speed of the cart begin to decrease at approximately: 3.5 minutes.

A typical time-speed graph shows the time on the x-axis and the speed on the y-axis. When the slope is rising, it means the speed is increasing. When the slope is horizontal, it means the speed is constant. When the slope falls or decline, it means speed is decreasing.

We are given a time-speed graph that shows the speed of a cart over a period of several minutes. Time in minutes is on the x-axis (horizontal axis) while speed in miles per hour is on the y-axis (vertical axis).

From the graph given, the speed of the cart started increasing up to about 3 minutes, since the line slopes upwards. Then, between 3 and 4 minutes, we have a horizontal line which starts to decline at approximately 3.5 minutes.

Therefore, we can conclude that the speed of the cart begin to decrease at approximately: 3.5 minutes.

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In the case above, the correct vectors are:

The solution for the Ship's vector are:

Note that the Horizontal aspect = 30 cos 30  

                                                   = 25.98.

For the  Vertical aspect = 30 sin(-30)

                                        = -15.

Hence it will be  <25.98, -15>.

In regards to the current's vector:

The Horizontal aspect=  5 sin 20

                                       = 1.71.

The Vertical aspect = 5 cos 20

                                     = 4.7.

Hence it will be <1.71, 4.7>.

Therefore, In the case above, the correct vectors are:

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Answer:??? rest of the question I think is what will be the exponent of 10 in the quotient? answer is 8

Step-by-step explanation:

Answer: 22.5

Step-by-step explanation:

[tex]\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5[/tex]

Answer: S=6√6 m².

Step-by-step explanation:

                                   Heron's formula

                            [tex]\displaystyle\\\boxed {S=\sqrt{p*(p-a)(p-b)(p-c)} }[/tex],

a, b, c - sides of a triangle,

[tex]\displaystyle\\p=\frac{a+b+c}{2}[/tex]

S - triangle area.

a=7 m,  b=5 m,  c=6 m.

[tex]p=\frac{7+5+6}{2} \\p=\frac{18}{2} \\p=9 (m).[/tex]

Hence,

[tex]S=\sqrt{9*(9-7)*(9-5)*(9-6)}\\S=3*\sqrt{2*4*3}\\S=3*2*\sqrt{2*3} \\S=6\sqrt{6} \ (m^2).[/tex]

Answer:

Step-by-step explanation:

Obtuse, greater than 90 degrees

Answer:

It should be an obtuse angle

Step-by-step explanation:

Well, it just is

Answer:

[tex]2x - 3 + \frac{1}{x-1}[/tex]

Step-by-step explanation:

Attachment :)

We use long division

Answer:

288 cm³

Step-by-step explanation:

cuboid formular: lengtg×width×height

Answer:

V = 288 cm³

Step-by-step explanation:

the volume (V) of a cuboid is calculated as

V = length × width × height

  = 8 × 9 × 4

  = 72 × 4

  = 288 cm³

Step-by-step explanation:

Solution

verified

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Correct option is A)

In an isosceles right angled triangle, the two sides on the right angle are equal.

Let the equal sides be a.

Hence, hypotenuse of the isosceles right angled triangle =

a

2

+a

2

=

2

a

Given, perimeter of the triangle =(6+3

2

)m

⇒a+a+

2

a=(6+3

2

)m

⇒a(2+

2

)=3(2+

2

)m

⇒a=3m

In the isosceles right triangle, the base and height =a

Hence, area of the triangle =

2

1

×base×height =

2

1

×3×3=4.5m

2

Add up the number of students within the random sample data:
32+26+28+22 = 108

We can then use proportional fractions / cross-multiply to answer the question.

In a sample size of 108 students, 32 of them preferred Movie A.
There are 900 students in total.

[tex]\frac{32}{108} =\frac{x}{900}[/tex]

32*900 = 28800

108*x = 108x

108x = 28800

x = [tex]266\frac{2}{3}[/tex] or [tex]\frac{800}{3}[/tex]

In decimal form that is approximately 266.667 and round that to the nearest whole number, you get 267 students who would prefer Movie A.

The statements that are true are;

The central angle measure created by the shaded region is 40°.

The ratio of the measure of ∠LOM to the measure of the whole circle is One-ninth.  

Circle O can be divided into a total of 9 sectors equal in area to sector LOM.

A central angle can be defined as an angle whose vertex is the center O of a circle and whose radii intersecting the circle in two distinct points

Note that;

The two radii are L O and MO

The measure of the angle is 40°

The sector is LOM

From the information given, it can be deduced that the 2 radii that forms the central angle is depicted by the shaded region which is said to have an angle of 40°. The sum of Circle O is one that can be shared into  9 equal sectors and that can be also equal in area to sector that is marked LOM

It can also be deduced that the circle can be divided into 9 equal sectors.

Thus, the statements that are true are;

The central angle measure created by the shaded region is 40°.

The ratio of the measure of ∠LOM to the measure of the whole circle is One-ninth.  

Circle O can be divided into a total of 9 sectors equal in area to sector LOM.

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Answer: A,C,D

Step-by-step explanation:

Answer:

slope = - 1 , y- intercept = 2

Step-by-step explanation:

calculate the slope m using the slope formula

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

with ( x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (2, 0) ← 2 points on the line

m = [tex]\frac{0-2}{2-0}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1

the y- intercept is the point on the y- axis where the line crosses , so

y- intercept = 2

Answer:

Slope: -1

Y-intercept: 2

Step-by-step explanation:

The line crosses the y-axis at 2. and the slope would be -1 since going down by one unit, and the line going down would mean that it is negative.

I hope it helps! Have a great day!

bren~

The perimeter of the trapezoid is 18 lines

Formula for perimeter of a trapezoid is given as;

Perimeter = a + b+ c + d

a = 1

b = 4

c = 4

d = 9

Perimeter = 1 + 4 + 4 + 9

Perimeter = 18

Thus, the perimeter of the trapezoid is 18 lines

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There are multiple strategies we can use to find the diameter of a circle. For this question, we must calculate the length of the radius first and multiply by 2 to find the diameter.

We're given the centre and a point on the circumference: [tex](-2,1),(6,7)[/tex].

Find the distance between them using the distance equation:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Plug in the given points:

[tex]d=\sqrt{(-2-x_1)^2+(1-y_1)^2}\\d=\sqrt{(-2-6)^2+(1-7)^2}\\d=\sqrt{(-8)^2+(-6)^2}\\d=\sqrt{64+36}\\d=\sqrt{100}\\d=10[/tex]

Therefore, the radius of the circle is 10 units.

Multiply the radius by 2 to find the length of the diameter:

10 × 2

= 20

Therefore, the length of the diameter is 20 units.

20 units

The value of equation 4-2(x+7)=3(x+5) is that x=-5/7.

Given equation 4-2(x+7)=3(x+5)

We are required to  solve the equation for the value of variable x.

Equation is relationship between two or more variables expressed in equal to form.Equation of two variables looks like ax+by=c. It can be a linear equation,quadratic equation, cubic equation. It can be solved for finding the value of variables.

The given equation is 4-2(9x+2)=3(x+5)

It is a linear equation.

We have to first remove the brackets by multiplying the numbers to inside numbers.

4-18x-4=3x+15

Now collect variable x at one end and constant at other end.

-18x-3x=15-4+4

-21x=15

x=-15/21

x=-5/7

Hence the solution of equation 4-2(x+2)=3(x+5) is that x=-5/7.

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The equivalent equation of the given equation is 39x - 45 = 15x - 24.

Hence, option C) is the correct answer.

Given the equation; 3[x + 3(4x – 5)] = 15x – 24

We expand and collect like terms

3[x + 3(4x – 5)] = 15x – 24

3( x + 12x - 15 ) = 15x - 24

3x + 36x - 45 = 15x - 24

We add the like terms on both sides

39x - 45 = 15x - 24

Therefore the equivalent equation of the given equation is 39x - 45 = 15x - 24.

Hence, option C) is the correct answer.

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