Factorisation of ax^2 + bx + c

Answer:

Jason's collection: 21 books.

Nathan's collection 24 books.

Step-by-step explanation:

Let number of books owned by Jason be j books and that for Nathan be n books.

So we have the system:

6j + 1/3 n = 134.........(1)

1/3j + n = 31................(2)

Multiply the first equation by -3. We get:

-18j - n = -402............(3)

Adding (2) + (3):

-53/3 j = -371

j = -371 * 3 / -53

j =  21.

Now substitute j = 21 in equation (2):

1/3(21) + n = 31

n = 31 - 7 = 24

n = 24.

Answer:

[tex]LA=755\ m^{2}[/tex], [tex]SA=785\ m^{2}[/tex]

Step-by-step explanation:

Part 1) Find the lateral area of the given prism

we know that

The lateral area of the prism is equal to

[tex]LA=PL[/tex]

where

P is the perimeter of the triangular base

L is the length of the prism

Find the perimeter P

[tex]P=5+6+11.21=22.21\ m[/tex]

we have    

[tex]L=34\ m[/tex]

substitute

[tex]LA=(22.21)(34)=755\ m^{2}[/tex]

Part 2) Find the surface area of the given prism

we know that

The surface area of the prism is equal to

[tex]SA=2B+LA[/tex]

where

B is the area of the triangular base

LA is the lateral area of the prism

Find the area B

[tex]B=(1/2)(5)(6)=15\ m^{2}[/tex]

we have

[tex]LA=755\ m^{2}[/tex]

substitute

[tex]SA=(2)(15)+755=785\ m^{2}[/tex]

The total cost y varies directly with the number of hours x needed to complete a job, with a direct variation coefficient of 100.

When analyzing the variation between two variables, specifically how y varies with x, we consider whether the relationship is direct or inverse. In the scenario provided, where it takes 10 workers 24 hours to do a job, if we let x represent the number of hours it takes to get the job done and y represent the total cost to the customer, we can establish that as the number of hours increases, the total cost also increases, assuming workers are paid by the hour. This suggests a direct variation.

Given that widget workers receive $10 per hour, the cost y to the customer for x hours of work would be 10 workers × $10 per hour × x hours. So, y = 10 × 10 × x = 100x. Hence, the relationship between y and x is directly proportional with a coefficient of variation of 100.

You may consider a function with domain [tex](0,\infty)[/tex] and switch [tex]x\mapsto -x[/tex]

For example, we know that

[tex]y=\log(x)[/tex]

can only be evaluated for positive values of the argument. This means that

[tex]y=\log(-x)[/tex]

can also be evaluated only for positive values of the argument, i.e.

[tex]-x>0 \iff x<0 \iff x \in (0,\infty)[/tex]

To give another example, you may consider a function with domain [tex][0,\infty)[/tex], consider its inverse to remove 0 from the domain, and finally switch again [tex]x\mapsto -x[/tex]:

[tex]\sqrt{x} \implies D = [0,\infty)\\\dfrac{1}{\sqrt{x}} \implies D = (0,\infty)\\ \dfrac{1}{\sqrt{-x}} \implies D = (-\infty,0)[/tex]

Answer:  13

Step-by-step explanation:  1st - Distribute the -1 through to the x + -1*(5+x) first:  8 + -1*[x + -1*(5+x)] = 8 + [-1*x  +  -1*-1*(5+x)]

= 8 + [-x + -1*-1 *(5+x)]

Multiply the two -1s that are in front of the (5+x).  Negative x Negative = positive

Minus the paranthesis

Do PEDMAS

8 + [-x + 5 + x]  <- -x +x = 0

                = 8 + [0 + 5]  <- 0 and 5 are like terms and will be combined

                = 8 + 5 = 13

The angle of 110° and the angle labelled as 1 form 180°, so we have

[tex]<1> = 180-110=70[/tex]

The same holds for the angle labelled 2 and the 115° angle:

[tex]<2> = 180-115=65[/tex]

Angle 1, 2 and 7 are the interior angles of a triangle, so they sum to 180. We can deduce

[tex]<7> = 180-70-65=45[/tex]

Angles 5 and 7 are corresponding angles, so they have the same measure.

Answer:

[tex]x=44[/tex]

Step-by-step explanation:

[tex]\frac{x}{4}+4=15 \\ \\ \frac{x}{4}=11 \\ \\ x=44[/tex]

Answer:

(x, y ) → (x - 8, y + 11)

Step-by-step explanation:

L(7, - 3) and L'(- 1, 8)

The x-coordinate 7 → - 1 , that is a shift of - 8

The y- coordinate - 3 → 8, that is a shift of + 11

The rule to translate LMN → L'M'N' is

(x, y ) → (x - 8, y + 11 )

Answer: D

Step-by-step explanation:

For this case we must find the product of the following expressions:

[tex]\frac {3x} {x + 1} * \frac {x} {x-7}[/tex]

So:

[tex]\frac {3x ^ 2} {x ^ 2-7x + x-7} =\\\frac {3x ^ 2} {x ^ 2-6x-7}[/tex]

So, we have to:

[tex]\frac {3x} {x + 1} * \frac {x} {x-7} = \frac {3x ^ 2} {x ^ 2-6x-7}[/tex]

Answer:

[tex]\frac {3x ^ 2} {x ^ 2-6x-7}[/tex]

Option C

Answer:

y=9x+1.6

Step-by-step explanation:

bring the 10.6 over by adding it to both sides

Answer:

bro ur wrongf its y – 10.6 = 9(x – 1)

Step-by-step explanation:

BRO U BOT

Answer:

[tex]64.3=\frac{1}{3}(B)(7)[/tex]

Step-by-step explanation:

we know that

The volume of a cone (bird feeder) is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base

h is the height of the cone

In this problem we have

[tex]V=64.3\ cm^{3}[/tex]

[tex]h=7\ cm[/tex]

substitute

[tex]64.3=\frac{1}{3}(B)(7)[/tex]

[tex]192.9=(B)(7)[/tex]

[tex]B=192.9/(7)=27.56\ cm^{2}[/tex]

The equation that can be used to determine the area of the circular lid needed to cover the bird feeder is 64.3 = 1/3 x b x 7.

A cone is a three-dimensional shape that consists of a circular base and a vertex.

Volume of a cone = 1/3πr²h

Area of a circle = πr²

πr = 64.3 = 1/3 x b x 7

To learn more about the volume of a cone, please check: https://brainly.com/question/13705125

#SPJ5

Answer:

17.4 i believe

Step-by-step explanation:

B is your answer hope it helps

Answer:

Step-by-step explanation:

Look at the picture.

It's a net of right rectangular prism.

We have three pairs of rectangles:

7ft × 8ft

7ft × 18ft

8ft × 18ft

The formula of an area of a rectangle l × w:

A = lw

Calculate the areas:

A₁ = (7)(8) = 56 ft²

A₂ = (7)(18) = 126 ft²

A₃ = (8)(18) = 144 ft²

The Surface Area :

S.A. = 2A₁ + 2A₂ + 2A₃

Substitute:

S.A. = 2(56) + 2(126) + 2(144) = 652 ft²

You must use Pythagorean theorem, which is [tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are both legs (the two legs are the sides that form a perpendicular right angle) while c is the hypotenuse (side opposite the right angle)

In this case...

a = y

b = 8

c = 12

^^^Plug these numbers into Pythagorean theorem

[tex]y^{2} +8^{2} =12^{2}[/tex]

Simplify as much as possible

[tex]y^{2}[/tex] + 64 = 144

Isolate y by subtracting 64 to both sides

[tex]y^{2}[/tex] + (64 - 64) = 144 - 64

[tex]y^{2}[/tex] = 80

Further isolate y by taking the square root of both sides. This will take away the square from the left side

y = [tex]\sqrt{80}[/tex]

[tex]\sqrt{80}[/tex] <<< Can be further simplified

4√5 = y

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

i would say b

Step-by-step explanation:

Answer:

b: cylinder

Step-by-step explanation:

because it's shaped like one

Answer:

C. [tex]f(x)=\sqrt[3]{-x} -1[/tex]

Step-by-step explanation:

Consider graph of the parent function (red curve in attached diagram)

[tex]g(x)=\sqrt[3]{x}[/tex]

First, multiply it by -1 to get function

[tex]h(x)=-\sqrt[3]{x}[/tex]

Then translate the graph of the function h(x) 1 unit down, then you'll get the function

[tex]f(x)=-\sqrt[3]{x} -1\\ \\ \text{or}\\ \\f(x)=\sqrt[3]{-x} -1[/tex]

The graph of the function f(x) is represented by the blue curve in attached diagram

The trim is the frame minus the glass.

[tex]A = (5x+3)(x+6) - (4x^2 + 26x + 15)[/tex]

[tex] = 5x^2+33x+18 - 4x^2 -26x - 15[/tex]

[tex] =x^2+7x+3[/tex]

Answer: Choice A

Answer with Step-by-step explanation:

A window frame has a length of (5x + 3) inches and a width of (x + 6) inches.

Area of window frame=(5x+3)(x+6)

                                    = 5x(x+6)+3(x+6)

                                    = 5x²+30x+3x+18

                                   = (5x²+33x+18) square inches

area of the glass in the window is (4x² + 26x + 15) square inches.

Area of trim around the glass=Area of window frame-Area of glass

                                                = 5x²+33x+18-(4x²+26x+15)

                                                =5x²-4x²+33x-26x+18-15

                                                =(x²+7x+3) square inches

Hence, Correct option is:

A. (x² + 7x + 3) square inches

There is 336 ways the runners can finish first, second, and third.

Answer:

Yes, the answer provided is correct.

Step-by-step explanation:

Angles TRV and SRW are vertical angles, so they are the same value.

Answer:

42.5%

Step-by-step explanation:

Answer:

42.5

Step-by-step explanation:

34/80×100/1

=340/8

=42.5

His sister is 8 and he is 20.

let's say z represents liz. we can make an equation where z+12=4z.

Solve for that and z is equal to 4. Now that was 4 years ago. She should be 8 now?

I hope this is correct because my brain isn't doing so well today.

Answer:

Adam is 20 years old and Liz is 8 years old.

Step-by-step explanation:

Let present age of Adam = x years

Let present age of Liz = y years

Now we will make the equations.

x = y + 12 -------------(1)

For second equation

( x-4) = (y-4) × 4

x-4 = 4y - 16

x = 4y + 4 - 16

x = 4y - 12 -----------------(2)

By substitution method, we  substitute  the value of  x  from equations (1) to equation (2).

y + 12 = 4y - 12

y - 4y + 12 = -12

-3y = -12 -12

3y = 24

y = 8

Now we put the value of y in equation (1)

x = 8 + 12 = 20

Therefore, Adam is 20 years old and Liz is 8 years old.

Answer:

Two solutions.

Step-by-step explanation:

[tex] \sqrt{x + 10} - 1 = x \\ \sqrt{x + 10} = x + 1 \\ (x + 10) = (x + 1) {}^{2} \\x + 10 = {x}^{2} + 2x + 1[/tex]

Answer:

hi so finding the volume you need to do

pi times R² times height

Step-by-step explanation:

hopes this will help u  outttttt

Use the slope-intercept form y = mx + b to find the slope m and y intercept 'b'

Y - Intercept: 5

(Slope:) -3/4

To find the y intercept you must make x zero and solve for y:

3(0) + 4y = 20

0 + 4y = 20

4y/4 = 20/4

y = 5

This means that the y intercept is:

(0, 5)

Hope this helped!

Answer:

25.8

Step-by-step explanation:

114 ft ---> 31 inches

114 ft = 1368 inches

31/1368=0.02266081871 inch scale model

95 feet = 1140 inches, so 1140 * the scale factor of 0.02266081871= 25.83333..

This means, to the nearest tenth inch, the wingspan of the scale model is 25.8

The wingspan of the scale model is approximately 25.8 inches when calculated using the scale factor based on the model's length and the actual length of the plane, both in inches.

To find the wingspan of the scale model, we need to set up a proportion based on the scale between the actual size and the model size of the plane. First, we will find the scale factor by comparing the actual length of the plane to the length of the model in the same units:

Actual length of plane: 114 ft

Model length of plane: 31 inches

We must convert the actual length into inches because the model is measured in inches (1 foot = 12 inches) 114 feet × 12 inches/foot = 1368 inches

The scale factor is the ratio of the model length to the actual length.

Scale Factor = Model Length / Actual Length in inches = 31 inches / 1368 inches

Now, to find the wing span of the model, we use the same scale factor:

Actual wingspan of plane: 95 ft

95 ft × 12 inches/ft = 1140 inches (Actual wingspan in inches)

Model Wingspan = Actual Wingspan in inches × Scale Factor

= 1140 inches × (31 inches / 1368 inches)

We calculate this to get the model's wingspan in inches and round it to the nearest tenth of an inch:

Model Wingspan = (1140 × 31) / 1368 ≈ 25.8 inches

Therefore, the wingspan of the scale model is approximately 25.8 inches when rounded to the nearest tenth.

Answer:

$445.32

Step-by-step explanation:

see picture attached

i hope this helped !!

Answer:

The area of rectangle C is 2

Step-by-step explanation:

Using a scale factor of [tex]\frac{1}{5}[/tex] yields the side lengths of 1 and 2

[tex](1)(2)=2[/tex]

Answer:

2 square units

Step-by-step explanation:

hello

The scale factor or linear scale factor is the ratio between the length of the same side in two similar figures.

in the graph we have  a rectangle with width 5 units and long 10 units, and we know the scale factor is 1/5

[tex]S_{f}=\frac{width(C)}{width(B)}\\ \\Width(B)*S_{f} =width(C)=5 units *\frac{1}{5} \\\\Width(C) =\frac{5}{5} units =1 unit[/tex]

[tex]S_{f} =\frac{length (C)}{length(B)} \\\\\\length(C)=length(B)*S_{f}\\length(C)=(10*\frac{1}{5})[/tex]

[tex]Length(C) =2 units\\\\ the area is A=w*l\\\\A=1 unit * 2 units\\\\\\[/tex]

A=2 square units

I hope it helps

We can use the law of cosines as follows:

[tex]7^2 = 8^2+10^2-2\cdot 8 \cdot 10 \cdot \cos(\theta)[/tex]

We can rewrite this equation as

[tex]49 = 164-160 \cdot \cos(\theta) \iff 160 \cdot \cos(\theta) = 115 \iff \cos(\theta)=\dfrac{115}{160}\approx 0.72[/tex]

For this case we have by definition of the Cosines Law that:

[tex]7 ^ 2 = 10 ^ 2 + 8 ^ 2-2 (10) (8) [/tex]* cosΘ

[tex]49 = 100 + 64-160[/tex]cosΘ

[tex]49 = 164-160[/tex]cosΘ

[tex]49-164 = -160[/tex]cosΘ

[tex]-115 = -160[/tex]cosΘ

[tex]115 = 160[/tex]cosΘ

cosΘ= [tex]\frac {115} {160} = 0.71875[/tex]

Rounding off we have, 0.72

ANswer:

Option C