Unfortunately, due to a couple of pitiful people (some poor kids who got so lost in life, they resulted to spamming), I’m having to repost this:

OK, so I was learning about how to factorize a quadratic polynomial. And I also wrote notes on it. Now, even though I know that my notes are definitely correct, I’m getting stuck at a certain point. Please look at the attached photo, and explain why the variable X and the number 4 have been removed when we get the factors. I’d greatly appreciate it. Thanks!

Answer:

6 sec

Step-by-step explanation:

when ball return to the ground, h is 0

0=at^2 +bt

0 = -4.9t^2+29.4t

factor: -4.9 times -6 is 29.4

0 = -4.9t(t-6)

set each equation to 0

-4.9t = 0 or t-6=0

t = 0 or t= 6

it's 6 seconds

Answer:

after 6 seconds in the air

Step-by-step explanation:

setting 'h' equal to zero will yield when the ball returns to the ground

you can factor out -4.9t to get:

-4.9t(t - 6) = 0

t = 0 (prior to ball being thrown)

t = 6 (this means, after 6 seconds, the height of the ball is back to zero)

Answer:

55°

Step-by-step explanation:

Thus from the atrachment, the angle PGR is 180°-35°-90°

= 55°

Answer:

The circumference of the back wheel is 2.62 inches

Step-by-step explanation:

Given

[tex]d_1 = 5in[/tex] --- diameter of front wheel

[tex]d_1 : d_2 = 3:1[/tex] --- ratio of the diameters

Required

The circumference of the back wheel

First, we calculate the diameter of the back wheel.

We have:

[tex]d_1 : d_2 = 3:1[/tex]

Substitute: [tex]d_1 = 5in[/tex]

[tex]5in: d_2 = 3 : 1[/tex]

Express as fraction

[tex]\frac{d_2}{5in} = \frac{1}{3}[/tex]

Make [tex]d_2[/tex] the subject

[tex]d_2 =5in * \frac{1}{3}[/tex]

[tex]d_2 = \frac{5}{3}\ in[/tex]

So, the circumference (C) of the back wheel is:

[tex]C =\pi d[/tex]

[tex]C = 3.14 * \frac{5}{6}\ in[/tex]

[tex]C = \frac{3.14 * 5}{6}\ in[/tex]

[tex]C = \frac{15.7}{6}\ in[/tex]

[tex]C = 2.62\ in[/tex]

Problem 27)

Refer to the diagram that says "problem 27".

This is the graph of y = 5x where x is the time in years, and y is the amount of simple interest in the account.

This equation comes from the simple interest formula below

i = P*r*t

i = 100*0.05*x

i = 5x

y = 5x

Note: The graph is a straight line through (0,0) and (1,5)

=====================================================

Problem 28)

The abscissa is the x coordinate. For a point like (-3, -7), the abscissa is -3.

The ordinate is the y coordinate. For that point mentioned earlier, the ordinate is -7.

The graph of points is shown below in the figure labeled "problem 28".

When graphing any point, we always start at the origin (0,0) where the x and y axis meet up. Then for a point like (-3,-7) we move 3 units to the left on the x axis and 7 units down on the y axis to arrive at point A. The other points are plotted in a similar fashion. The labels A,B,C,D are optional. They were added to help keep track of the points.

Answer:

80

Step-by-step explanation:

Area of a square is LxL where L is the length of the side

so 6400 = LxL

L = 80

Answer:

I added some attachments as well, I hoped I helped.

1) angle RQP

2) angle PQR

Answer:

c.100

Step-by-step explanation:

first draw a figure of rhombus EFGH to avoid confusions

given

angle E= 3x+5

angle H= 4x

here,

E=G and H=F ( opposite angles of rhombus are equal)

now,

E+G+H+F= 360 ( sum of interior angles in a rhombus)

3x+5+3x+5+4x+4x= 360

x= 25°

we know that,

F= H

F= 4x

F= 4 × 25

F= 100

Answer:

h(x) is the image after f(x) is horizontally stretched by a scale factor of 4

Step-by-step explanation:

Given

[tex]h(x) = \frac{1}{4}x^2[/tex]

[tex]f(x) = x^2[/tex]

Required

Compare h(x) to f(x)

We have:

[tex]h(x) = \frac{1}{4}x^2[/tex]

Substitute [tex]f(x) = x^2[/tex]

[tex]h(x) = \frac{1}{4}f(x)[/tex]

This means that f(x) is stretched horizontally by a scale factor of 4 to get h(x)

Answer:

A. the first possible case is always n = 1

Step-by-step explanation:

Mathematical induction is a technique used to provide proof for a statement such that the statement holds for all natural numbers which are the non-negative integers

Therefore, given that the natural numbers are 0, 1, 2..., we have that mathematical induction can start from n = 0

Therefore, the statement which is not true is that the first possible case is always n = 1

Answer:

(0,8)

Step-by-step explanation:

Let X be 0 and solve for Y to get the intercept

y= - 4([tex]10^{x}[/tex]) + 12

y= - 4 * [tex]10x^{0}[/tex] + 12

y= - 4 * 1 + 12

y= - 4 + 12

y=8

when x=0, y=8

(0,8) is y intercept

The y-intercept of the given function is (0,8).

We have given that,

The graph of the function f(x) = 10^x

The y-intercept of function gif g(x)=4f(x) + 12

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Let X be 0 and solve for Y to get the intercept

[tex]y= - 4(10^x) + 12[/tex]

[tex]y= - 4 (10^0) + 12[/tex]

[tex]y= - 4 * 1 + 12[/tex]

[tex]y= - 4 + 12[/tex]

[tex]y=8[/tex]

when x=0, y=8

The y-intercept of the given function is (0,8).

To learn more about the intercept visit:

https://brainly.com/question/1884491

#SPJ5

Answer:

2

Step-by-step explanation:

Parallel lines have the same slopes

If the slope of line a is 2, the slope of line b is 2

Answer:

slope of line b = 2

Step-by-step explanation:

The slopes of parallel lines are equal

Given slope of line a = 2 and parallel to line b , then

slope of line b = 2

Answer:

$8

Step-by-step explanation:

12.5 hours earned him $110

then an hour will earn him less

12.5=$110

1=x then you cross multiply

12.5x=110

12.5x/12.5=110/12.5

x=8

therefore an hour will earn him $8

Answer:

Step-by-step explanation:

1). 3x + 10

3(2) + 10

= 16

2). 14 - 2y

14 - 2(-3)

= 20

3). 7x - 5y

7(2) - 5(-3)

= 29

4). 5x + 7

5(2) + 7

= 17

5). 2x + 3y

2(2) + 3(-3)

= -5

6). 6y - 5x

6(-3) - 5(2)

= -28

Given:

In the first year, the car will decrease in value by 25%.

The cost of a car is Rs. 200,000.

To find:

The worth of the car after 1 year.

Solution:

The cost of a car is Rs. 200,000 and in the first year the car will decrease in value by 25%. So, the worth of the car after 1 year is:

[tex]Worth=200000-\dfrac{25}{100}\times 200000[/tex]

[tex]Worth=200000-\dfrac{1}{4}\times 200000[/tex]

[tex]Worth=200000-50000[/tex]

[tex]Worth=150000[/tex]

Therefore, the worth of the car after 1 year is Rs. 150,000.

Step-by-step explanation:

am-an+bm-bn

m(a+b)-n(a+b)

(m-n)(a-b)

Answer:

[tex] \small \sf \: ( m - n ) ( a + b )[/tex]

Step-by-step explanation:

( am - an + bm - bn)

= ( am - an ) + ( bm - bn )

= a ( m - n ) + b ( m - n )

= ( m - n ) ( a + b )

Answer: m∠x = 40°

Step-by-step explanation:

This works the exact same way as the other one

Being adjacent angles in a parallelogram, the two angles would be supplementary (add up to 180°).

140° + x° = 180°

x = 40°

Answer: Start at the positive

x

-axis, then rotate left by the desired angle.

Explanation-

Standard position means the first arm of the angle is the positive

x

-axis, and the other arm is placed by rotating counter-clockwise from there, by the amount of the angle.

As a basic example, the symbol

∠

is about a 45° angle in standard position.

To get a feel for where the second arm (called the "terminal arm") will go, remind yourself that the axes themselves meet each other at 90°.

If our angle was 90°, the terminal arm would be on the positive

y

-axis.

If our angle was 180°, it would be on the negative

x

-axis.

Wait! 180° is more than 150°, so our angle is somewhere in quadrant 2. In fact, 150° is 2/3 of the way between 90° and 180°, so our terminal arm will be 2/3 of the way into quadrant 2.

graph{(y+tan(pi/6)x)(y^2-.00001x)=0 [-10, 10, -5, 5]}

(ignore the part of the line in quadrant 4)

Answer:

5%

Step-by-step explanation:

5 customers ordered large cold drinks so the probability would be 5/100

To convert 5/100 to percent, just do 5/100 x 100%

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]a-3b+4[/tex]

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying the Equation...}}\\\\\frac{1}{2}(2a-6b+8)\\----------------\\\rightarrow\frac{1}{2}* 2a = a\\\\ \rightarrow\frac{1}{2}*-6b = -3b\\\\\rightarrow\frac{1}{2}*8 = 4\\\\\text{\underline{Therefore:}}\\\\\frac{1}{2}(2a-6b+8)\rightarrow \boxed{a-3b+4}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer: a-3b+4

Step-by-step explanation:

Credits to guy up there

Answer:

T.S.A = 233.29 cm²

volume of the cone = 235.84 cm³

Step-by-step explanation:

Given;

diameter of the cone, d = 9 cm

radius of the cone, r = 4.5 cm

slant height of the cone, l = 12 cm

The total surface of the cone is calculated as;

T.S.A = πr²  +  πrl

T.S.A = πr(r + l)

T.S.A = 3.142 x 4.5(4.5 + 12)

T.S.A = 233.29 cm²

The volume of the cone is calculated as;

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Where;

h is height of the cone

h² = 12² - 4.5²

h² = 123.75

h = √123.75

h = 11.12 cm

[tex]V = \frac{1}{3} \pi \times (4.5)^2 \times 11.12\\\\V = 235.84 \ cm^3[/tex]

Answer:

46%

Step-by-step explanation:

x : 100 = 23 : 50

x = (23 * 100)/50 = 46%

Answer:

the average probability of all possible outcomes of a future event occurring, weighted by each possible outcome individually

Step-by-step explanation:

An experiment can be defined as an investigation which typically involves the process of manipulating an independent variable (the cause) in order to be able to determine or measure the dependent variable (the effect).

This ultimately implies that, an experiment can be used by scientists to show or demonstrate how a condition causes or gives rise to another i.e cause and effect, influence, behavior, etc in a sample.

In Statistics, an expected value can be defined as the average probability of all possible outcomes of a future event occurring in an experiment, weighted by each possible outcome individually. Thus, an expected value in theory refers to the outcome an individual expect to obtain from an experiment in the long-run.

Mathematically, an expected value can be calculated by summing the products of each distinct outcome and their probability respectively.

Answer:

The last number line or D.

Step-by-step explanation:

To find the remaining coats to be collected, subtract the coats that are collected from the total of coats needed.

So:

78 - 13= 65

They must collect a total of 65 and more to break the last year's record of 78 coats. Number line D, represents the solution of this inequality.

Hope this helps! Have a nice dayy! :)

Answer:

A = 24

Step-by-step explanation:

Figure shown is a trapezoid

Area of a trapezoid = [tex]\frac{a+b}{2} h[/tex]

where a and b = base lengths and h = height

The trapezoid shown has the following dimensions

Shorter base length (a) = 6

Longer base length (b) = 10

Height (h) = 3

Using these dimensions , plug in the values into the area formula

A = [tex]\frac{6+10}{2} 3[/tex]

add 6 + 10 = 16

[tex]A=\frac{16}{2} 3[/tex]

divide 16/2 = 8

[tex]A = (8)(3)[/tex]

multiply 8 times 3

A = 24

Answer:

In standard notation [tex]3.5 \times 10^4 = 35000[/tex]

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of 10.

----------------

If it was 3.5 x 104 it would equal 350.

Answer:

Their present age are 15 and 18

Step-by-step explanation:

a : b = 5 : 6

[tex]\frac{a}{b} = \frac{5}{6} \\\\6a = 5b\\\\a = \frac{5b}{6} \\\\\frac{a-3}{b-3} = \frac{4}{5} \\\\5(a-3) = 4(b-3)\\\\5a - 15= 4b - 12\\\\5a - 4b = 15 - 12\\\\5a - 4b = 3\\\\substitute \ the \ value \ of \ a \ into \ the \ above \ equation;\\\\5(\frac{5b}{6} ) - 4b = 3\\\\25b - 24b = 18\\\\b = 18\\\\now, \ solve \ for \ a;\\\\a = \frac{5}{6} \times 18\\\\a = 15[/tex]