Mathematics High School

Hi can I have help on this question with a simple explanation as I find things difficult to understand. Thank you :)

Answers

Answer 1

Step-by-step explanation:

Line L → 2x - 3y = 6

Where a = 2 and b = -3

• So, we can use this formula to find the gradient of Line L.

m = -a/b

m = -2/-3

m = 2/3 IS THE ANSWER

Answer 2

Answer:

gradient = 2/3

Step-by-step explanation:

Here is another way....manipulate the equation to y = mx+ b form

where m = slope ( gradient)

2x - 3y = 6 add 3 y to both sides

6 + 3y = 2x subtract 6 from both sides

3y = 2x - 6 divide by 3

y = 2/3 x - 2 gradient = 2/3

Related Questions

express 80 as a product of its prime factors, write the prime numbers in accending order

Answers

Answer:

80 as a product of prime numbers can be expressed as 2×2×2×2×5

The circumference of a circle is 237 cm.
What is the area, in square centimeters?
Express your answer in terms of T.

Answers

Answer:

Circumference of a circle = 2 pie r

237 = 2 * pie * r

237 / 2 * Pie

118.5/ pie = r

118.5 = Pie*r

Area of circle = Pie *r²

= Pie r * r

= 118.5 * 118.5/ Pie

= 118.5 * 118.5 / pie

= 14042.25/ pie

taking value of pie = 3.14

= 4472.05 sq. cm

A quilt is designed using a square pattern. Each square contains two rectangles. Each rectangle contains a shaded rhombus.

Each rectangle contains a shaded rhombus. The left angle is 50 degrees and the top angle is (2 x + 20) degrees.

What is the value of x?

50
55
125
145

Answers

According to the computations, this rhombus's value of x is equal to 55°.

How can we calculate x's value?

The total of all the angles in a rhombus should be 360 ° because the opposing angles in a rhombus are always identical.

We may infer the preceding information from the rhombus's picture:

Neighboring angles= 2x+ 20 & 50°

Opposite angles=2x+ 20 & 50°

Combining the angles results in:

2x+20+50+2x+20+50=360

⇒4x+140= 360

⇒4x=360-140

⇒4x=220

⇒x=220/4

⇒x=55°

Hence, it is concluded that the value of x is (b) 55°.

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1. Decide if the following is a properly formed syllogism. If you are going to wrap Holly’s gift, you need wrapping paper. If you need wrapping paper, you have to go to the store. Therefore, if you go to the store, then you’re going to wrap Holly’s gift.

A) This is a syllogism.

B) This is not a syllogism.

Answers

This is not a syllogism. Hence option B is correct.

What is a syllogism?

A logical structure for a formal argument that includes a major, minor, and conclusion.

This syllogism cannot be concluded without a given statement.

You'll need wrapping paper if you're going to wrap Holly's present. To get wrapping paper, you must visit a store.

Therefore, you will wrap Holly's present if you visit the store. This isn't a syllogism

Hence option B is correct.

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Answer:

This is not a syllogism

Step-by-step explanation:

I took the quiz. :)

evaluate the following expression when x=-4 and y=4
x³-x /4y[tex]\frac{x}{y}[/tex]

Answers

Answer: - 60

Step-by-step explanation:

[tex]\frac{(-4)^3 - (-4)}{4(4)^-4/4} \\\\= -60[/tex]

PLEASE HELP. FUNCTIONS AND RELATIONS. PROVIDE ANSWER OPTION A,B,C OR D? THANKS!!

Answers

Step-by-step explanation:

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12. How many grams is of of 800 g?
[tex] \frac{3}{8} [/tex]

of 800 g ?

Answers

Answer:

800

Step-by-step explanation:it's cuz g represents

3/8 of 800g is 300g

3/8 converted to decimal = 0.375 x 800g
= 300g

A dial combination lock has dials numbered 0 to 5. The lock is set to an even number. How many different numbers could it be?

I need some help on this one, anyone know?

Answers

The number of combinations will be 6 for even numbers.

What is the combination?

The arrangement of the different things or numbers in a number of ways is called the combination.

Given that:-

A dial combination lock has dials numbered 0 to 5. The lock is set to an even number. How many different numbers could it be?

The total sample numbers are from 0 to 5 which are 0,1,2,3,4,5.

The even numbers are 0,2,4.

The combinations will be given by:-

C = 3!

C = 3 x 2 x1

C = 6

Therefore the number of combinations will be 6 for even numbers.

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In the diagram Below

Answers

Answer:

∠UTC = 55°∠UCD = 70°∠BCT = 55°

Step-by-step explanation:

In this figure of overlapping parallelograms, each angle is related to the others by several different theorems involving triangles, parallelograms, and parallel lines. That is, there are several different ways one can arrive at the answers to this question.

UTC

∠UTC ≅ ∠UDC = 180° -∠EDU . . . opposite angles of parallelogram; linear pair

∠UTC = 180° -125° = 55°

UCD

∠UCD ≅ ∠TBC = 180° -∠TBA . . . . corresponding angles; linear pair

∠UCD = 180° -110° = 70°

BCT

∠BCT ≅ ∠UTC = 55° . . . . alternate interior angles

Suppose that F(x) = x² and G(x) = 3x^2 + 8. Which statement best compares the graph of G(x) with the graph of F(x)?

A. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units to the left.

B. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units to the left.

C. The graph of G(x) is the graph of F(x) compressed vertically and
shifted 8 units up.

D. The graph of G(x) is the graph of F(x) stretched vertically and
shifted 8 units up.

Answers

Answer:

The graph of G(x) is the graph of F(x) stretched vertically and shifted 8 units up.

p varies jointly as q and the square of r, and p = 200 when q = 2 and r = 3. Find p when q = 5 and r= 2.

Answers

Step-by-step explanation:

If a variables varies jointly, we can just divide it by the other variables in relation to it.

For example, since p variables jointly as q and square of r, then

[tex] \frac{p}{q {r}^{2} } = k[/tex]

where k is a constant

First, let find k. Substitute p= 200

q= 2, and r=3.

[tex] \frac{200}{2(3) {}^{2} } = k[/tex]

[tex] \frac{200}{18} = k[/tex]

[tex] \frac{100}{9} = k[/tex]

Now, since we know our constant, let find p.

[tex] \frac{p}{q {r}^{2} } = \frac{100}{9} [/tex]

Q is 5, and r is 2.

[tex] \frac{p}{5( {2}^{2}) } = \frac{100}{9} [/tex]

[tex] \frac{p}{20} = \frac{100}{9} [/tex]

[tex]p = \frac{2000}{9} [/tex]

Can anyone help me with this

Fnd the value of x.

x = ?

Answers

Answer:

X=62 degrees

Step-by-step explanation:

The solution is in the image

Answer:

62°

Step-by-step explanation:

We know that the sum of the interior angles in a triangle is added up to 180°.

Therefore,

68.5° + 49.5° + x = 180°

118° + x° = 180°

x = 180° - 118°

x = 62°

NEED HELP ON THIS ASAP!!!!!!

Answers

Answer: Choice B (If you need to do questions like this in the future i recommend using the desmos graphing calculator online, inputting the equations and comparing them)

There are 12 ducks and 11 geese in a certain park. Find the ratio of geese to ducks.

Answers

Answer:

11:12

Step-by-step explanation:

You first have to put the number of geese to ducks in a ratio form and since 11 and 12 have no common factors one cannot reduce the ratio

Given the quadrilateral below is a rhombus, solve for the length of the side of the rhombus.

Answers

Answer:

7.21

Step-by-step explanation:

There is a formula to find the area of a side of a rhombus given 2 diagonals.

It is: [tex]\frac{\sqrt{p^{2}+q^{2} } }{2}[/tex]

64 + 144 = 208

[tex]\sqrt{208}[/tex] = 14.42

14.42 / 2 =

7.21

The diagonals of the rhombus meet perpendicularly, so you have four right triangles. Because of this you can use the Pythagorean theorem with 8 and 12 to find the side.

Theorem: a^2 + b^2 = c^2

8^2 + 12^2 = c^2
64+144 = c^2
c^2 = 208
c = sqrt208

You’re planning to place an order from an online boutique. Leggings are $12 each and shipping is a flat rate of $5. Write an expression that represents the total cost of your order (not including tax) based on the number of leggings (l) you buy.

Answers

Answer:

For the cost of each legging to be $12, and the shipping of $5, the expression is a straight line C = 12x + 5 where x is the number of leggings.

Step-by-step explanation:

It is given that each legging costs $12. This means that for x number of leggings, the cost will be $12x. Now there is an additional cost of shipping that is $5. So, total cost will be a linear equation and can be written as

C = 12x + 5

This equation represents a straight line like y = mx + c. Here y = C, m = 12 and c = 5.

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Find the y-intercept of the rational function.

A (0, -10)
B (-10, 0)
C (0 , -2)
D (-2, 0)

Answers

Answer:

Step-by-step explanation:

The y intercept is when the graph passes the y axis. This occurs at (0,-2)

Mark's Digital Place has a compact digital camera at a price of $425, a 8 inch tablet for $540 and a
game console for $610. If you want to get an additional three years warranty, then you need to pay
15% extra on the original price and $50.
Daphne wants to buy a digital camera and a tablet to start a photography course. When she went into
the store, she found that the store id offering a discount of 5% on the camera and 80 on the tablet.
Daphne also want the additional three years warranty. How müch money does Daphne need to pay to
buy both the items with a three years additional warranty on each item?

Answers

Answer:

jjxfzhfxjgjhzjjjtxjxjxktxjtxjtxtxh

In which funtion is x=2 mapped to 32?

Answers

The function g(x)=4(x+3)² - 68 is mapped to 32.

What is equation?

An equation is a mathematical expression in terms of one or more unknown variable.

Given are the following functions:

f(x)= - 3x² - 4

g(x)= 4(x+3)²-68

f(x)= 3x

f(x)= 2x-62

To get the mapped function, we substitute the value of x in all function,

a) f(x)=-3x²- 4

Put x=2,

f(2)= -3 (2)² - 4

f(2)= -16

It is not mapped.

b) g(x)=4(x+3)² - 68

Put x=2,

g(2) = 4(2+3)² - 68

g(x) =32

It is mapped to 32.

c) f(x)=3x

Put x=2,

f(2) = 3 x 2 =6

It is not mapped.

d) f(x)=2x - 62

Put x=2,

f(2) =2x2 -62

f(2) = -58

It is not mapped.

Therefore, the function g(x)=4(x+3)² - 68 is mapped to 32.

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The additive inverse of an element of x of a set is the number, which when added to x gives the answer 0. In the set {-3, -2, -1, 0, 1, 2, 3}, what is the additive inverse of -2?

Answers

Answer:

Step-by-step explanation:

the additive inverse of - 2 is 2 , since

- 2 + 2 = 0

How do u solve 3/8+1/8-2/7+1/4

Answers

Answer:

13/28

Step-by-step explanation:

using pemdas we can determine that the equation is directly solves from left to right

first

we have

3/8 + 1/8

which is 4/8

you can simplify this to 1/2

then you have 1/2 - 2/7

you must make them have the same numerator

you can multiple 1/2 by 7/7 and 2/7 by 2/2

7/14 - 4/14 = 3/14

now you must add 3/14 and 1/4

but you to make them have the same numerator

so you multiply 3/14 by 2/2 and 1/4 by 7/7

6/28 + 7/28 = 13/28

that is your final answer

Preform the indicated operation.
(2x+y)(3 x² + y)

Answers

Answer:

[tex]6x^3+3x^2y+2xy+y^2[/tex]

Step-by-step explanations:

[tex](2x+y)(3x^2+y)\\2x*3x^2+2xy+3x^2y+y*y - Distribute\\6x^3+3x^2y+2xy+y^2 - Simplify[/tex]

Answer:

6x^3 + 2xy + 3x^ 2y + y^2

Step-by-step explanation:

Apply the distributive property of multiplication. First multiply (3x^2 + y) by 2, obtaining 6x^3 + 2xy, and then multiply (3x^2 + y) by y, obtaining

3x^2y + y^2. Finally, combine like terms (if any) in these two results:

6x^3 + 2xy + 3x^ 2y + y^2

Reece and Sarah share some money in the ratio 9 : 16.
Reece says that Sarah gets more than 60% of this money. Show that Reece is correct.

Answers

Answer:

64% > 60%

Step-by-step explanation:

Total Units = 9 + 16 = 25 units.

Sarah Receives 16 units out of 25.

Percentage = 16/25 * 100

= 64%

Therefore Sarah received more than 60% of this money and therefore Reece is correct.

Which expression can be used to convert 22 Australian dollars to US dollars?

Assume 1.2 Australian dollars equals 1 US dollar.

Answers

Answer:

1.2x = 22x = 55/3 ≈ 18.3322 AUD = 18.33 USD

Step-by-step explanation:

1 USD - 1.2 AUD

x USD - 22 AUD

cross multiply

1.2 · x = 1 · 22

1.2x = 22

multiply both sides by 10

12x = 220

divide both sides by 12

x=55/3 ≈ 18.33

USD - United States dollar

AUD - Australian dollar

7. Miguel draws a square on a coordinate plane. One vertex is located at (5, 4). The
length of each side is 3 units. Circle the letter by all the ordered pairs that could be
another vertex.
A. (5, 1)
B. (5, 7)
C. (7, 8)
D. (2, 6)
E. (2, 1)

Answers

Answer:

A, B and E

Step-by-step explanation:

Answer: A,B and E i did the test

Step-by-step explanation:

A group of 328 people consists of men ,women, and children. There are five times as many men than children and twice as many women then children. How many women are there

Answers

Step-by-step explanation:

Ultimately we know:

Men = * 5

Women = * 2

Children =

We can already make the estimation that the amount of children will be below 50. So by trial and error you will get to your answer by substituting with 41.

Children - 41

Women - 41 x 2 = 82

Men - 41 x 5 = 205

205 + 41 + 82 = 328

So your answer is 41

if cos^4+cos^2=1 prove that cot^4a-cot^2a=1

Answers

Step-by-step explanation:

We can solve this kind of trigonometric problem

easily by the followings method :

Given :

cos^4a + cos^2a = 1

or, cos4^a = 1 - cos^2a

Therefore; cos^4a = sin^2a

Again,

To prove: cot^4a - cot^2a = 1

L.H.S = Cot^4a - cot^2a

= Cos^4a÷ sin^4a - Cos^2a ÷ sin^2a

= Sin^2a ÷ Sin^4a - cos^2a ÷ Sin^2a

= 1 ÷ Sin^2a - cos^2a ÷ Sin^2a

= 1 - cos^2a ÷ Sin^2a

= Sin^2a ÷ Sin^2a

= 1 = R.H.S proved.

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can someone please help mee

Answers

Answer:

x = -2y

y-intercept: ( 0, 0 ) and slope: [tex] \frac{1}{2} [/tex]

cotpheta•sin2pheta=

1+cos2pheta
1+cospheta
1+sin2pheta

Answers

Answer:

Step-by-step explanation:

Did you mean.

[tex] = \cot( \theta) . \sin(2 \theta) [/tex]

[tex] = \frac{ \cos( \theta) }{ \sin( \theta) } .(2 \sin( \theta) \cos( \theta) )[/tex]

[tex] = \frac{2 \sin( \theta) \cos {}^{2} ( \theta) }{ \sin( \theta) } [/tex]

[tex] = 2 \cos {}^{2} ( \theta) [/tex]

[tex] = 2.(1 - \sin {}^{2} ( \theta) )[/tex]

[tex] = 2 - 2 \sin {}^{2} ( \theta) [/tex]

No option Solution.

A biologist is studying the effects of using a type of bacteria to clear drain pipes. She creates a simulation of a typical kitchen drain system and
uses it regularly for three days before introducing the bacteria. She then carries out her simulation for another 15 days.
The population of bacteria can be approximated using function b, where dis the number of days since she started the experiment and (d) is the
bacteria population in hundreds.
b(d) = √5.2d-15.6 +2
Use this information to complete the statement.
The domain over which the bacteria population Increases is

Answers

The domain over which the bacteria population Increases is [tex]d \ge 3[/tex]

How to determine the domain?

The function is given as;

[tex]d = \sqrt{5.2d - 15.6} + 2[/tex]

Set the radicand greater than or equal to 0

[tex]5.2d - 15.6 \ge 0[/tex]

Add 15.6 to both sides

[tex]5.2d \ge 15.6[/tex]

Divide both sides by 5.2

[tex]d \ge 3[/tex]

Hence, the domain over which the bacteria population Increases is [tex]d \ge 3[/tex]