I need 51-55 Thanks You :D no

I Need 51-55 Thanks You :D No

Answers

Answer 1

Answer:

Below

Step-by-step explanation:

All figures are squares. The area of a square is the side times itself

Let A be the area of the big square and A' the area of the small one in all the 5 exercices

51)

● (a) = A - A'

A = c^2 and A' = d^2

● (a) = c^2 - d^2

We can express this expression as a product.

● (b) = (c-d) (c+d)

■■■■■■■■■■■■■■■■■■■■■■■■■■

52)

● (a) = A-A'

A = (2x)^2 = 4x^2 and A'= y^2

● (a) = 4x^2 - y^2

● (b) = (2x-y) ( 2x+y)

■■■■■■■■■■■■■■■■■■■■■■■■■■

53)

● (a) = A-A'

A = x^2 and A' = y^2

● (a) = x^2-y^2

● (b) = (x+y) (x-y)

■■■■■■■■■■■■■■■■■■■■■■■■■■

54)

● (a) = A-A'

A = (5a)^2 = 25a^2 and A' =(2b)^2= 4b^2

● (a) = 25a^2 - 4b^2

● (a) = (5a-2b) (5a+2b)

■■■■■■■■■■■■■■■■■■■■■■■■■■

55)

● (a) = A - 4A'

A = (3x)^2 = 9x^2 and A'= (2y)^2 = 4y^2

● (a) = 9x^2 - 4 × 4y^2

● (a) = 9x^2 - 16y^2

● (a) = (3x - 4y) (3x + 4y)


Related Questions

Find the length of AB

Answers

Answer:

AB = 3π

Step-by-step explanation:

The formula for the circumference of a circle is:

C = 2πr

By substituting 27 for r:

C = 2π(27)

C = 54π

The whole circumference is 54π. A circle is 360º around. We can set up a proportion to find the length of the 20º arc:

[tex]\frac{360}{54p}[/tex] = [tex]\frac{20}{x}[/tex]

Cross-multiply:

360x = 1080π

Divide both sides by 360:

x = 3π

AB = 3π

Answer:

AB = 3π

Step-by-step explanation:

The arc AB can be calculated as

AB = circumference of circle × fraction of circle

The central angle is equal to the measure of arc AB = 20° , thus

AB = 2πr × [tex]\frac{20}{360}[/tex]

     = 2π × 27 × [tex]\frac{1}{18}[/tex] ( cancel 18 and 27 by 9 )

     = 2π × 3 × [tex]\frac{1}{2}[/tex] = 6π × [tex]\frac{1}{2}[/tex] = 3π

The area of a square of side 2.4 cm is​

Answers

Answer:

area of cube = a^2  ( a is side)

2.4^2 = 5.76 cm^2

Answer:

5.76 cm^2

Step-by-step explanation:

Hey there!

Well if the side length is 2.4 cm then the area would be,

A = l•l

A = 2.4 • 2.4

A = 5.76cm^2

Hope this helps :)

The figure below shows a parallelogram ABCD Side AB parallel to side DC and side AD is parallel to side BC A student wrote the following sentences to prove that parallelogram ABCD has two pairs of opposite sides equal For triangles and COB alternate interior angle ABD is congruent to angle CDB because AB and DC are parallel lines Similarly interior angle equal to angle CBD because AD and are parallel lines equal to DB by the reflexive property Therefore , triangles ABD and COB are congruent by the SAS postulate Therefore AB congruent to and AD congruent BC CPCTC Which statement best describes a flaw in the student's proof ?

Answers

Answer:

Second choice

Explanation :

The postulate that is used in order to prove the congruency of the triangles is the ASA which means (Angle – Side – Angle). The property that is applicable for the congruency of DB to itself is the reflexive property. Therefore, the answer to this item is the second choice.

Hope I helped! :)

If yes mark me BRAINLIEST!

Tysm!

Triangles ABD and CDB are congruent to each other by the ASA theorem. The student used SAS which is wrong. The answer is: D.

What is the ASA Theorem?

The ASA theorem states that two triangles that have a pair of corresponding included congruent sides and two pairs of corresponding congruent angles are congruent triangles.

Based on the ASA theorem, triangles ABD and CDB are congruent to each other.

Therefore, the use of SAS theorem by the student is wrong.

Learn more about the ASA theorem on:

https://brainly.com/question/2102943

#SPJ6

Solve the triangle. A = 51°, b = 14, c = 6, I'll give 20 points

Answers

Answer:

Step-by-step explanation:

We have that

A = 51°, b = 14, c = 6

step 1

find the value of a

Applying the law of cosines

a²=c²+b²-2*c*b*cos A

a²=6²+14²-2*6*14*cos 51-------> 126.27

a=11.2

we know that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

we have

a=11.2

b=14

c=6

so

(a+b) > c-------------> (11.2+14)=25.2

25.2 > 6-----> is not correct

therefore

the answer is the option

a. No triangles possible

I don't know if i am right sorry if this is wrong

S(t) = -105t + 945 to determine the salvage value, S(t), in dollars, of a table saw t years after its purchase. How long will it take the saw to depreciate completely? A. 11 years B. 8 years C. 7 years D. 9 years

Answers

Answer:

D

Step-by-step explanation:

When something depreciates completely, it will have a total value of 0 dollars. Therefore, set the equation to zero and solve for t to find the years.

[tex]S(t)=-105t+945\\0=-105t+945\\-105t=-945\\t=9[/tex]

Therefore, the table saw will completely depreciate after 9 years.

Answer:

[tex]\large \boxed{\sf \bold{D.} \ 9 \ years}[/tex]

Step-by-step explanation:

[tex]S(t) = -105t + 945[/tex]

For the value to depreciate completely, the amount has to be equal to 0 dollars.

Set S(t) to 0.

[tex]0 = -105t + 945[/tex]

Solve for the time t.

Subtract 945 from both sides.

[tex]0 -945= -105t + 945-945[/tex]

[tex]-945=-105t[/tex]

Divide both sides by -105.

[tex]\displaystyle \frac{-945}{-105}=\frac{-105t}{-105}[/tex]

[tex]9=t[/tex]

It will take 9 years for the saw to depreciate completely.

An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 3028 feet and Plane B is at an altitude of 4000 feet. Plane A is gaining altitude at 55.75 feet per second and Plane B is gaining altitude at 35.5 feet per second. How many seconds will pass before the planes are at the same altitude? seconds What will their altitude be when they're at the same altitude? feet

Answers

Consider plane A with respect to B,

initial relative Altitude [tex] h_{a, b}=h_a-h_b=-972 [/tex]

relative rate of altitude(speed) $r_{a,b}= 55.75-35.5=20.25$

To get at same altitude, they'll take same time, and their relative height will be $0$ So,

$H_{a,b}=h_{a,b}+r_{a,b}t$

$0=-972+20.25t$

$t=48$

and altitude will be, $3028+55.75\cdot 48=5704$

Answer:

48 seconds5704 feet

Step-by-step explanation:

We can write equations for the altitude of each plane:

  A(t) = 3028 +55.75t . . . . . initially at 3028 ft; gaining at 55.75 ft/s

  B(t) = 4000 +35.5t . . . . . initially at 4000 ft; gaining at 35.5 ft/s

The two altitudes will be equal when ...

  A(t) = B(t)

  3028 +55.75t = 4000 +35.5t . . . . substitute the expressions for A and B

  20.25t = 972 . . . . . . subtract 3028+35.5t

  t = 48 . . . . . . . . . . . . divide by 20.25

The common altitude will be ...

  B(48) = 4000 +35.5(48) = 5704 . . . . feet

The planes will both be at an altitude of 5704 feet after 48 seconds.

Point B lies between points A and C, and all three points lie on point AC, which of the following is not true? A. Point B lies on segment AC B. Point C lies on ray AB C. Point A lies on ray BC D. Point C lies on line AB

Answers

Answer:

C. Point A lies on ray BC

Step-by-step explanation:

Points A and C can be connected by a segment which would be a measure of the distance between the points. Locating point B between AC, makes the three points lying on segment AC.

A ray extends from a point to infinity, a line extend to infinity on both sides, while a segment is known to have two endpoints. Therefore, points AC are the end points of the segment AC, and point B between this segment confirms that point B lies on the segment AC. Therefore, Point A lies on ray BC is not correct.

What is the difference between a coefficient and variable (such as 3x) and a constant (5)?  Why can these two types of terms not be combined?
 

Answers

Answer:

see below (I hope this makes sense!)

Step-by-step explanation:

Constants, as the name suggest, stay constant, meaning that their value never changes. For example, 2 will always be 2 and 9.4 will always be 9.4. On the other hand, the values of variables can change. Take, for example, the variable 2x. When x = 1, 2x = 2 and when x  =2, 2x = 4 so the value of 2x can change depending on what x is. You can't combine constants and variables because they are not like terms, basically, one can change and the other can't and you cannot combine terms that are not like each other.

Claire and Richard are both artists who use square canvases. Claire

uses the polynomial 50%? + 250 to decide how much to charge for her paintings

and Richard uses the polynomial 40x² + 350 to decide how much to charge for

his paintings. In each polynomial, x is the height of the painting in feet.

a. How much does Claire charge for a 20-foot-tall painting?

b. How much does Richard charge for a 15-foot-tall painting?

c. To the nearest tenth, for what height will both Claire and Richard charge

the same amount for a painting? Explain how to find the answer.

d. When both Claire and Richard charge the same amount for a painting,

how much does each charge?

Answers

Answer:

A.  [tex]Claire = 20250[/tex]

B.   [tex]Richard = 9350[/tex]

C.    Height = 3.2 feet

D. Charges = $760

Step-by-step explanation:

Given

[tex]Claire = 50x^2 + 250[/tex]

[tex]Richard = 40x^2 + 350[/tex]

Solving (a): Claire's 20ft charges

In this case, x = 20

Substitute 20 for x in [tex]Claire = 50x^2 + 250[/tex]

[tex]Claire = 50(20)^2 + 250[/tex]

[tex]Claire = 50(400) + 250[/tex]

[tex]Claire = 20000 + 250[/tex]

[tex]Claire = 20250[/tex]

Solving (b): Richard's 15ft charges

In this case, x = 15

Substitute 20 for x in [tex]Richard = 40x^2 + 350[/tex]

[tex]Richard = 40(15)^2 + 350[/tex]

[tex]Richard = 40(225) + 350[/tex]

[tex]Richard = 9000 + 350[/tex]

[tex]Richard = 9350[/tex]

Solving (c): Height which they both charge the same;

This implies that

[tex]50x^2 + 250 = 40x^2 + 350[/tex]

Solving for x [Collect Like Terms\

[tex]50x^2 - 40x^2 = 350 - 250[/tex]

[tex]10x^2 = 100[/tex]

Divide both sides by 10

[tex]x^2 = 10[/tex]

Take square roots of both sides

[tex]x = \sqrt{10}[/tex]

[tex]x = 3.2ft[/tex]  (Approximated)

Hence; Height = 3.2 feet

Solving (d): How much they charge when the charge the same amount.

Substitute 3.2 for x in any of the given equation

[tex]Claire = 50x^2 + 250[/tex]

[tex]Claire = 50(3.2)^2 + 250[/tex]

[tex]Claire = 50*10.24 + 250[/tex]

[tex]Claire = 512 + 250[/tex]

[tex]Claire = 762[/tex]

[tex]Richard = 40x^2 + 350[/tex]

[tex]Richard = 40(3.2)^2 + 350[/tex]

[tex]Richard = 40 * 10.24 + 350[/tex]

[tex]Richard = 409.6 + 350[/tex]

[tex]Richard = 759.6[/tex]

The reason for the difference is due to approximation

Hence, they both charge approximately 760

Factor completely x3 + 8x2 − 3x − 24. (x − 8)(x2 − 3) (x + 8)(x2 + 3) (x − 8)(x2 + 3) (x + 8)(x2 − 3)

Answers

Answer:

(x + 8) (x² - 3)

Step-by-step explanation:

Given:

x³ + 8x² - 3x - 24

Find:

Factors

Computation:

x³ + 8x² - 3x - 24

x²(x + 8) -3(x + 8)

(x + 8) (x² - 3)

Factor of the given equation is (x + 8) (x² - 3)

Answer:

(x + 8) (x² - 3)

Step-by-step explanation:

Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5 cups of sugar, and the brownie recipe requires 1.25 cups of sugar. Write an addition equation to represent the total amount of sugar Dante needs. Enter your answer as an addition equation, like this: 42+(-53)=-11

Answers

Answer:

2.75 cups of sugar

Step-by-step explanation:

Hello!

To find the total amount of sugar Dante needs we need to add the amount need for each recipe

Cookie recipe needs 1.5 cups

Brownie recipe needs 1.25 cups

1.5 + 1.25 = 2.75 cups of sugar

The answer is 2.75 cups of sugar

Hope this helps!

Answer:

the answer is 1.5+1.25=1.75

Step-by-step explanation:

i just added them together

your welcome ( it also depends on how many times he uses the recipes)

If the Cost price of the an article is greater than the selling price, we have a ____?​

Answers

Answer:

loss

Step-by-step explanation:

Selling an item for less than was paid gives a loss

Selling an item for more than was paid gives a profit

it a cycle is sold for rs 17250 there is again of rs 2250. what is the gain percentage ​

Answers

Answer:

15%

Step-by-step explanation:

profit=sp -cp

cp=sp-profit

=17250-2250

=15000

profit%= profit amount/cp *100%

=2250/15000×100

= 15

Answer:

[tex] \boxed{ \boxed{ \sf{ \bold{ \purple{15\%}}}}}[/tex]

Step-by-step explanation:

Given,

SP ( Selling price ) = Rs 17250

Profit ( P ) = Rs 2250

CP ( Cost price ) = Rs 17250 - Rs 2250 = Rs 15000

Now, let's find the profit / gain percentage :

Profit % = [tex] \sf{ \frac{profit}{cost \: price} \times 100\%}[/tex]

plug the values

⇒[tex] \sf{ \frac{2250}{15000} \times 100\%}[/tex]

Calculate

⇒[tex] \sf{15\%}[/tex]

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

▪[tex] \underline{ \underline{ \sf{ \blue{What \: is \: the \: formula \: to \: find \: profit \: percent \: and \: loss \: percent?}}}}[/tex]

We know that , profit and loss are calculated on cost price ( CP ). So, profit percent and loss percent can be calculated by using the following formula :

[tex] \boxed{ \sf{Loss\% \: = \frac{cp - sp}{cp} \times 100\%}}[/tex]

[tex] \boxed{ \sf{ \bold{Profit\% \: = \: \frac{sp \: - \: cp}{cp} \times 100}}}[/tex]

Hope I helped!

Best regards!!

HELP!!!
The solutions to (x + 3)^2- 4=0 are x = -1 and x = -5

True or false

Answers

Answer:

False

Step-by-step explanation:

We can simplify this equation and then solve for x.

[tex](x+3)^3-4=0\\\\x^2+6x+9-4=0\\\\x^2+6x+5=0\\\\(x+2)(x+3)=0\\\\x=-3\\x=-2[/tex]

As you can see, the solutions are not x=-1 and x=-5.

Therefore, the answer is false.

Answer:

True

Step-by-step explanation:

Given

(x + 3)² - 4 = 0 ( add 4 to both sides )

(x + 3)² = 4 ( take the square root of both sides )

x + 3 = ± [tex]\sqrt{4}[/tex] = ± 2 ( subtract 3 from both sides )

x = - 3 ± 2

Thus

x = - 3 - 2 = - 5

x = - 3 + 2 = - 1

G(x)= -\dfrac{x^2}{4} + 7g(x)=− 4 x 2 ​ +7g, left parenthesis, x, right parenthesis, equals, minus, start fraction, x, squared, divided by, 4, end fraction, plus, 7 What is the average rate of change of ggg over the interval [-2,4][−2,4]open bracket, minus, 2, comma, 4, close bracket?

Answers

Answer:

-1/2

Step-by-step explanation:

Given the function [tex]G(x)= -\dfrac{x^2}{4} + 7[/tex], the average rate of change of g(x) over the interval [-2,4], is expressed as shown below;

Rate of change of the function is expressed as g(b)-g(a)/b-a

where a - -2 and b = 4

[tex]G(4)= -\dfrac{4^2}{4} + 7\\G(4)= -\dfrac{16}{4} + 7\\G(4)= -4 + 7\\G(4) = 3\\[/tex]

[tex]G(-2) = -\dfrac{(-2)^2}{4} + 7\\G(-2)= -\dfrac{4}{4} + 7\\G(-2)= -1 + 7\\G(-2)= 6[/tex]

average rate of change of g(x) over the interval [-2,4] will be;

[tex]g'(x) = \frac{g(4)-g(-2)}{4-(-2)}\\ g'(x) = \frac{3-6}{6}\\\\g'(x) = -3/6\\g'(x) = -1/2[/tex]

Find the measure of each angle indicated. Round to the nearest tenth.

A) 65.20
C) 55.1°
B) 51°
D) 55.70​

Answers

Answer:

51

Step-by-step explanation:

Answer: D) 55.7 degrees approximately

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

The reference angle has AC = 12.3 as the opposite side and BC = 8.4 as the adjacent side. The tangent ratio ties the opposite and adjacent sides together.

--------

tan(angle) = opposite/adjacent

tan(theta) = AC/BC

tan(theta) = 12.3/8.4

theta = arctan(12.3/8.4)

theta = 55.6697828044967

theta = 55.7 degrees approximately

--------

arctan is the same as inverse tangent which is written as [tex]\tan^{-1}[/tex]

make sure your calculator is in degree mode

Draw a line for the axis of symmetry of function f. Also mark the x-intercept(s), y-Intercept, and vertex of the function.
f(x)= x^2- 4x-5
+
10-
Line
8
6
4
2-
-10
-8

Answers

Answer:

1) Please find attached the graph sowing the line of symmetry

The symmetry line is a vertical line passing through (2, -9)

2) The x-intercept are (5, 0) and (-1, 0)

The y-intercept is (0, -5)

The vertex is (2, -9)

Step-by-step explanation:

The given function is;

f(x) = x² - 4·x - 5

The data values are generated as follows;

x,          f(x)

-1,         0

-0.8,    -1.16

-0.6,    -2.24

-0.4,    -3.24

-0.2,    -4.16

0,         -5

0.2,      -5.76

0.4,      -6.44

0.6,     -7.04

0.8,     -7.56

1,         -8

1.2,      -8.36

1.4,      -8.64

1.6,      -8.84

1.8,      -8.96

2,        -9

2.2,     -8.96

2.4,      -8.84

2.6,     -8.64

2.8,     -8.36

3,        -8

3.2,     -7.56

3.4,     -7.04

3.6,     6.44

3.8,     -5.76

4,        -5

4.2,      -4.16

4.4,     -3.24

4.6,     -2.24

4.8,      -1.16

5,           0

The minimum is found from differentiating the function, f(x), with respect to x and looking for the zeros of the result  as follows;

f'(x) = 2·x -4

f'(x) = 0 = 2·x -4

x = 2

The y-coordinate gives; f(2) = 2² - 4×2 - 5 = -9

Therefore, the symmetry line is a vertical line passing through (2, -9)

The x-intercept is the point at which y = 0, therefore, from f(x) = x² - 4·x - 5, we have;

0 = x² - 4·x - 5 = (x - 5)·(x + 1)  

Therefore, the x-intercept are x = 5 or -1

The x-intercept are (5, 0) and (-1, 0)

The y-intercept occur at the point where the x value = 0, therefore, we have;

The y-intercept occur at y = f(0) = 0² - 4·0 - 5 = -5

The y-intercept is (0, -5)

Re-writing the  equation in vertex form y = a(x - h)² + k gives;

f(x) = x² - 4·x - 5 = 1·(x - 2)² - 9

Therefore, the vertex is (2, -9)

Answer:

see attached graph

The x-intercept are (5, 0) and (-1, 0)

The y-intercept is (0, -5)

The vertex is (2, -9)

Step-by-step explanation:

On a coordinate plane, parallelogram H I J K is shown. Point H is at (negative 2, 2), point I is at (4, 3), point J is at (4, negative 2), and point K is at (negative 2, negative 3). HIJK is a parallelogram because the midpoint of both diagonals is __________, which means the diagonals bisect each other

Answers

Answer: HIJK is a parallelogram because the midpoint of both diagonals is (1,0) , which means the diagonals bisect each other.

Step-by-step explanation:

Given: The coordinates of parallelogram H I J K as

H is at (- 2, 2), point I is at (4, 3), point J is at (4, - 2), and point K is at (- 2, - 3).

Diagonals : HJ and IK  [join opposite vertices]

Mid point of HJ = [tex](\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

[tex]=(\dfrac{-2+4}{2},\dfrac{2+(-2)}{2})=(1,0)[/tex]

i.e. Mid point of HJ = (1,0)

Mid point of IK = [tex](\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]

[tex]=(\dfrac{4+(-2)}{2},\dfrac{3+(-3)}{2})=(1,0)[/tex]

i.e. Mid point of IK = (1,0) =Mid point of HJ

When mid points of both diagonals are equal then that means the diagonals bisect each other.

Thus, HIJK is a parallelogram because the midpoint of both diagonals is (1,0) , which means the diagonals bisect each other.

Answer:

(1,0)

Step-by-step explanation:

PLEASE help me solve this question! This is really URGENT! No nonsense answers please.

Answers

Answer:

[tex]\boxed{\sf 6.4 \ seconds}[/tex]

Step-by-step explanation:

t = time (s) ⇒ ?

d = distance falling (m) ⇒ 200 (m)

a = acceleration due to gravity ⇒ 9.8 (m/s²)

The time in seconds is not given. Solve for time using the formula.

[tex]t=\sqrt{\frac{2(200)}{9.8} }[/tex]

[tex]t=\sqrt{\frac{400}{9.8} }[/tex]

[tex]t= 6.388766...[/tex]

Round answer to nearest tenth of a second.

[tex]t \approx 6.4[/tex]

Kim is y years old. Jasper is twice as old as Kim, or 2y years old. Lorenzo is 2 years older than Jasper, or (2y + 2) years old. Finally, Vinnie is 9 years old. The sum of their ages is y + 2y + (2y + 2) + 9. What is an equivalent way to write this expression?

Answers

Answer:

5y+11

Step-by-step explanation:

y+2y+2y+2+9

5y+11

The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10
Find d when v=70​

Answers

Answer:

         d = 245

Step-by-step explanation:

d is directly proportional to the square of a speed v

d = av²

5 = a•10²

5 = 100a

a = 0.05

d = 0.05v²

d = 0.05•70²

d = 0.05•4900

d = 245

In a recent Super Bowl, a TV network predicted that 53 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 79 people who saw the commercials and found that 41 of them said they would watch one of the television shows.Suppose you have the following null and alternative hypotheses for a test you are running:H0:p=0.53H0:p=0.53Ha:p≠0.53Ha:p≠0.53Calculate the test statistic, rounded to 3 decimal places

Answers

Answer: -0.196

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

Explanation:

We're conducting a one proportion Z test.

The hypothesized population proportion is p = 0.53, which is not to be confused with the p-value (unfortunately statistics textbooks seem to overuse the letter 'p'). Luckily this problem is not asking for the p-value.

The sample population proportion is

phat = x/n = 41/79 = 0.518987 approximately

The standard error (SE) is

SE = sqrt(p*(1-p)/n)

SE = sqrt(0.53*(1-0.53)/79)

SE = 0.056153 approximately

Making the test statistic to be

z = (phat - p)/(SE)

z = (0.518987 - 0.53)/0.056153

z = -0.19612487311452

z = -0.196

Which is approximate and rounded to 3 decimal places.

what is nine and forty-two hundredths

Answers

Answer:

9.42

Step-by-step explanation:

Breaking the phrase down:

'Nine' would be the number 9 in the ones place.

'And' represents the decimal in a number. ('.')

'Forty-Two Hundredths" is 0.42.

So, "nine and forty-two hundredths" would be 9.42.

Hope this helps.

Consider the following system of equations: y=2x−2 6x+3y=2 The graph of these equations consists of two lines that: 1. intersect at more than one point. 2. intersect in an infinite number of points. 3. intersect at exactly one point. 4. do not intersect.

Answers

Answer:

3.  Intersect at exactly one point.  ( (2/3), (-2/3) )

Step-by-step explanation:

To make the comparison of these lines easier, let's rewrite the 2nd equation into slope-intercept form, as the 1st equation is in slope-intercept form.

[1] y = 2x - 2

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

[2] 6x + 3y = 2 ==> 3y = 2 - 6x ==> y = -2x + (2/3)

[2] y = -2x + (2/3)

So now that we have both equations in slope-intercept form, we can see that the two equations are both linear, have different slopes, and have different y-intercepts.

Since these equations have both different slopes and different y-intercepts, we know that the lines will cross at least one point.  We can confirm that the lines only cross at a single point using the fact that both equations are linear, meaning there will only be one point of crossing.  To find that point, we can simply set the equations equal to each other.

y = 2x - 2

y = -2x + (2/3)

2x - 2 = -2x + (2/3)

4x = (8/3)

x = (8/12) = (2/3)

And plug this x value back into one of the equations:

y = 2x - 2

y = 2(2/3) - 2

y = (4/3) - (6/3)

y = (-2/3)

Thus these lines only cross at the point ( (2/3), (-2/3) ).

Cheers.

Answer:

I don't understand the question

MATHEMATICS
SECTION A (VERY SHORT ANSWERS)
1. Which of the following is irrational?
a V25
V12
b. Vs
c.
V3
2. V768 in its simplest form is:
dve
16
a.
16 V3
b. 64 V3 c.4 V3
d. 8 V3
3. The simplest rationalisation factor of 27 is:
a. b. 73
c. 27
d. 3
4. If x=2 and y = 3, then the value of xy + yt is:
a. 15
b. 17
c. 19
d. 21
a
2
5. The value of [ 8-43 + 22/12 is:
b. 2 ch d. 4
6. If p(x) = x2 – 3x + 2, then what is the value of p(0) + p(2).
7. Find the value of k, if (2x - 1) is a factor of the polynomial 6x2 + kx - 2.
8. Expand (x - y)
9. If x11 + 101 is divided by (x + 1), then what remainder do we get?
10. Find the value of x2 + 3, if(x - 5) = 13
SECTION B (SHORT ANSWERS
11. Express 0.123 in the form where p and q are integers and qf0
9
√7-√6
12. Rationalise the denominator of
√ + √6
13. Find the value of x if
&2x
14. If x2 + = 7 then find x3 +
15. If x + y + z = 10 and x2 + y2 + z = 40 find xy + y2 + zx and x3 + y + z3 - 3xyz
16. Factorize 8x3 - (2x - y)3
81
16

Answers

1 is c
2 is d
3 is b
4 is c
5 is a

ASAP!!! PLEASE help me solve this question! No nonsense answers, and solve with full solutions.

Answers

Answer:

Option (4)

Step-by-step explanation:

By the theorem of inscribed angles and the intercepted arc,

"In a circle, angles subtended by the same arc always measure the same and the arc measures the double of the inscribed angle."

If an inscribed angle in a circle measures 75° then all inscribed angles by the same arc will measure 75°.

In addition to this, measure of arc subtended by these inscribed angle will measure double of the inscribed angle (150°)

Therefore, Option (4) will be the answer.

what is the coefficient of x in the equation of 32+2x=10
solve after finding the coefficient

Answers

Answer:

x= -11

Step-by-step explanation:

the coefficient is variable that appears before a number . bearing this in mind, the coefficient of x is therefore 2 .

the value of x is:

>32+2x=10

>2x=10-32

>2x= -22

>x= -11

Answer:

Step-by-step explanation:

Coefficient of x = 2

32 + 2x  = 10

Subtract 32 from both side

32 + 2x -32 = 10 - 32

              2x =  - 22

Divide both sides by 2

            2x/2 = -22/2

x = -11

In 2008, golfer Annika Sornestam had a driving accuracy of 71%. That is, on par 4 and par 5 holes, her tee shot landed in the fairway 71% of the time. Explain how to use a spinner to simulate Sorenstam’s performance in a round of golf where she attempts 15 drives. (Hint: What type of chart is a spinner? What does each piece represent?)

Answers

Answer:

Ok, we know that the driving accuracy is of 71%.

Then the first step is to get a spinner that is enumerated from 1 to 100 (in such way that each number is equispaced)

Now, we can mark a section between numbers 1 and 71. (this regio represents the cases where the shot lands in the fairway) and the unmarked region represents the cases where the shot does not land in the fairway.

Now, for each shot, we can spin our spinner next to a fixed pencil, depending on the section of the spinner that is marked by the pencil when the spinner fully stops, we can guess if the shot landed or not in the fairway.

In this way the shot has the region from 1 to 71 (71%) to land in the fairway

and the region from 72 to 100 to not land in the fairway.

If you want to simulate Sorenstam’s performance in a round of golf where she attempts 15 drives, you need to spin the spinner 15 times, and record the oucomes.

An orchardist is to plant apple trees and pear trees in the ratio 3:11. If he intends to plant 150 apple trees, how many pear trees will he need to plant?

Answers

The ratio 2:11 means for every 3 apple trees they will plant 11 pear trees.

They are planting 150 apple trees. Divide total apple trees by the ratio: 150/3 = 50

Multiply that by the ratio of pear trees:

50 x 11 = 550

They need to plant 550 pear trees.

Using the conversion 1 mile equals 1.6093 km to convert 4.9 kilometers to miles, round o the nearest tenth of a mile

Answers

Answer:

3.0 miles

Step-by-step explanation:

Using the conversion 1 mile equals 1.6093 km to convert 4.9 kilometers to miles, round to the nearest tenth of a mile.

1 mile = 1.6093 km

Convert 4.9km to mile

We can use cross multiplication :

Let the number of miles = m

1 mile = 1.6093 km

'm' miles = 4.9 km

Cross multiply :

m × 1.6093 = 4.9 × 1

m = 4.9 / 1.6093

m = 3.0448020 miles

Rounding 3.0448020 to the nearest tenth :

3.0 miles

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