Mathematics High School

Hi, anyone able to help with qn 7? Thanks :)!

Answers

Answer 1

Answer:

Step-by-step explanation:

I used the quadratic formula to find the roots of [tex]x^{2} + x -1[/tex]

[tex]a=\frac{-1-\sqrt{5}}{2} b=\frac{-1+\sqrt{5} }{2}[/tex]

[tex]\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} )^{2} * \frac{-1+\sqrt{5}}{2}[/tex]

[tex]\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * \frac{-1+\sqrt{5}}{2}*(\frac{-1-\sqrt{5}}{2} )[/tex]

[tex]\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * \frac{-1+\sqrt{5}-\sqrt{5} -4}{4}[/tex]

[tex]\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * \frac{ -4}{4}[/tex]

[tex]\frac{1 }{\sqrt{3} } *(\frac{-1-\sqrt{5}}{2} ) * -1[/tex]

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

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

Related Questions

What numbers would be in the in the 4 sections of a 2 x 2 array that shows the problem 18 x 17? 100, 80, 70, 15 10, 80, 70, 56 100, 80, 70, 56 100, 80, 7, 56

Answers

Answer:

100, 70, 80, 56

Explanation:

Look at attached image!

In the 2 x 2 array, the sum of all squares is 18 x 17 = 306.

The number in the 4 sections are 100, 80, 70, and 56.

A 2 x 2 array that shows the problem 18 x 17.

2 x 2 array has four blockers or magic quadrants, the matrix diagram is a simple square divided into four equal quadrants.

18 = 10 +8

17 = 10 +7

18 x 17 = 306

In the 2 x 2 array : 100+80+70+56 = 18 x 17 = 306

Therefore, In the 2 x 2 array, the sum of all squares is 18 x 17 = 306.

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Describe the products made by the process of cellular respiration.

Answers

Step-by-step explanation:

The product is carbon dioxide and water

10x=6x-24

help!!!! me pleasee!!

Answers

Answer:

x = -6

Step-by-step explanation:

10x = 6x - 24

Subtract 6x from both sides.

4x = -24

Divide both sides by 4.

x = -6

I will give brainliest! Please help!!

Answers

Roughly 3.0666. Hope this helps!!

Which represents the inverse of the function f(x) = 4x?

h(x) = x + 4
h(x) = x – 4
h(x) = three-quartersx
h(x) = one-quarterx

Answers

h(x) = one-quarter is the correct answer!

By definition, the correct answer is the last option: the inverse of the function f(x) = 4x is h(x)= [tex]\frac{1}{4}[/tex]x.

Definition of inverse function

The inverse or reciprocal function of f(x) is called another function f⁻¹(x) that satisfies: If f(x)=y , then f⁻¹(y)=x.

To build or calculate the inverse function of any function, one of the ways to do it is to interchange the variables x and y, and use a combination of algebraic methods in order to isolate the variable "y".

Inverse of f(x)=4x

Being f(x)=y=4x, to calculate the inverse, in first place you interchange the variables x and y:

f(y)=x=4y

Isolating the variable y, you get:

h(x)=x÷4= [tex]\frac{1}{4}[/tex]x

Finally, the correct answer is the last option: the inverse of the function f(x) = 4x is h(x)= [tex]\frac{1}{4}[/tex]x.

Learn more about the inverse of a function:

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Please help me answer number 12

Answers

Answer:

It is same.

The PS and RS leg which has the same length allow the use of HL by providing the same degree of angle.

Thank you and please rate me as brainliest as it will help me to level up

(05.01)
The graph of a system of equations with the same slope and the same y-intercepts will
have no solutions. (1 point)
O Always
Sometimes
O Never
Help ASAP

Answers

Answer:

Always

Step-by-step explanation:

Answer:

never.

Step-by-step explanation:

Find the length of AD

Answers

Answer:

What is the length of the BC line? It is not clear in the figure

Answer:

x=1

Step-by-step explanation:

as the two triangles are similar

So the equation is

5+x/12=5/10

50+10x=60

10x=60-50

10x=10

x=10/10

therefore

x=1

What would the graph of x > 5 look like?

Answers

Answer:

It will look like this

Can someone please help me with this question?!

Answers

Answer:

-5

Step-by-step explanation:

The slope is given by

m= ( y2-y1)/(x2-x1)

= ( 0-10)/(2-0)

= -10/2

= -5

What is the slope of the line in the graph?

Answers

Answer:

1/2

Step-by-step explanation:

went up one across two. rise over run y over x

Answer:

1/2

Step-by-step explanation:

Nick bought 6 tickets to an air show if he spent 156 dollars how much did the tickets cost

Answers

Answer:

$26 dollars

Step-by-step explanation: when you divide 156 divided by 6 you get 26

Answer:

26 dollars per ticket

Step-by-step explanation:

156/6=26

26x6=156

In order to make sure this value is correct we can substitute the value of x in the equation

[tex]2(1.55+0.7)=6(1.55-0.8)\\\Rightarrow 2\times 2.25=6\times 0.75\\\Rightarrow 4.5=4.5[/tex]

So, both sides are equal hence the value of [tex]x [/tex]is 1.55.

1. Which of the following lines is parallel to the line y = -3/2x +1 and contains the point (4,2)?

Answers

Answer:

The answer should be y = -[tex]\frac{3}{2}[/tex][tex]x[/tex] + 8, but its not one of the answers, so check the question again.

Step-by-step explanation:

If the second line is parallel, then the gradient will be the same:

y = -[tex]\frac{3}{2}[/tex][tex]x[/tex] + c

Find what c is (y-intercept) by inputting the given point into the equation (4,2):

2 = (-[tex]\frac{3}{2}[/tex] x 4) + c

2 = -6 + c

c = 8

what is the value of this expression below when w=10 and x=7
10w-7x

Answers

Answer:

=51

Step-by-step explanation:

10w - 7x

10(10) - 7(7)

100 - 49

=51

10*10=100
7*7=49
Then subtract:
100-49=51
So the answer is 51

Express Jenny's age in terms of a if jenny is three years less than half of Anne's age
Express Fraz's age in terms of a if Fraz is twice the sum of Anne's age and 7

Answers

1. a = 1/2x - 3
2. a = 2x + 7

The bottom of a ladder leaning against a wall is 1.5 m from the bottom of the wall. The ladder is 5.5 m long. Find how high the top of the ladder is above the ground, correct to one decimal place.

A. 5.8 m
B. 5.7 m
C. 5.2 m
D. 5.3 m

Answers

Answer: D. 5.3 m

Step-by-step explanation:

The ladder leaning against the wall causes it to forma right angle.

The right angle has two sides , which is the two legs, and the hypotenuse.

Using the formula a^2 + b^2 = c^2 , a and b are the two legs and c is the hypotenuse. In this case, a will be the wall, b will be 1.5 m and the ladder which is 5.5 m will be the hypotenuse.

Input the values for a and c to sole for b using the formula.

1.5^2 + b^2 = 5.5^2

2.25 + b^2 = 30.25

-2.25 -2.25

b^2 = 28

b = [tex]\sqrt{28}[/tex]

b = 5.2915 rounded to one decimal place is the same as rounding it to the nearest tenth, and 5.29 rounded to the nearest tenth is 5.3.

Height of top of ladder above the ground that is resting on the wall, correct to one decimal place is 5.3 m

hence option D is correct.

According to Pythagoras theorem

In a right triangle

[tex]\rm H^2 = P^2 + B^2[/tex]

[tex]\rm P = \sqrt {H^2 - B^2 }.........(1)\\where \\H = Hypotenuse \; of \; right\; triangle\\B = Base\; of \; the \; right\; triangle \\P = Perpendicular \; of \; the\; right\; triangle[/tex]

In the given situation the the ladder forms the right triangle with the wall

Length of the ladder = 5.5 m

Length of the base of ladder from the wall = 1.5 m

Let K be the height of top of ladder above the ground that is resting on the wall.

Hence from equation (1) we can write

[tex]\rm K = \sqrt{5.5^2 - 1.5^2} = \sqrt{28} = 5.291 \approx \bold{5.3}[/tex] m

Height of top of ladder above the ground that is resting on the wall, correct to one decimal place is 5.3 m

hence option D is correct.

For more information please refer to the link given below

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Simplify this expression using the distributive property

Answers

Answer:

When you use the distributive property, you multiply the two numbers together, just like simplifying any product. You will also see another example where the expression in parentheses is subtraction, rather than addition. You will need to be careful to change the sign of your product.

Step-by-step explanation:

[tex]\huge\boxed{\bold{\mathfrak{Hello\;there!}}}}}[/tex]

The Distributive Property states that

[tex]\dashrightarrow[/tex] [tex]\bold{a(b+c)=ab+ac}[/tex]

[tex]\dashrightarrow[/tex] We multiply a by b and c, and then add the two products.

Example:

[tex]\dashrightarrow[/tex] [tex]\bold{10(x-3)}[/tex]

[tex]\dashrightarrow[/tex] [tex]\bold{10x-30}[/tex]

[tex]\bold{I\;really\;hope\;it\;helps\;you!}[/tex]

[tex]\rm{Have\;a\;great\;day![/tex]

[tex]\boxed{AmiableTeen:)}[/tex]

The following graph represents the cost and revenue functions for custom-made computers. How many computers
have been sold at the break-even point?

a 12
b 9
C 5
d. 0

Answers

A it’s the answer correct

Answer:

A. 12

Step-by-step explanation:

А A
B
D
If m_ABD = 64°, and mZCBD = 30°,
then m ABC = [?]°

Answers

Answer:

34 degrees

Step-by-step explanation:

If ABD = 64, and CBD is 30, we can use PWP( Part Whole Postulate)

Step 1.CBD + ABC = ABD

Step 2. Substitute

30 + ABC = 64

Step 3. Isolate ABC

34 = ABC

ABC is 34 degrees

9514 1404 393

Answer:

34°

Step-by-step explanation:

It should be fairly intuitive that the two smaller angles add to give the value of the larger one. (Even if it's not, the angle sum theorem tells you this is true.)

∠ABC + ∠CBD = ∠ABD

∠ABC + 30° = 64°

∠ABC = 34° . . . . . . . . . subtract 30° from both sides of the equation

Sarah and her friends picked 3 3/4 pints of blueberries. After they ate some of the blueberries, only 2 1/3 pints remained.

How many pints of blueberries did Sarah and her friends eat?

Enter your answer, as a mixed number in simplest form, in the box.

Answers

Answer:

1 5/12

Step-by-step explanation:

subtract 3 3/4 - 2 1/3 and you get 1 5/12

Answer:

17/12

Step-by-step explanation:

I turned the two fractions into improper fractions and made them have the same denominators. Then I subtracted.

Find the mean absolute deviation of the set: 10,5,7,14,19,32,25

Answers

Answer: I believe it would be 8.

Step-by-step explanation:

consider the line y=9x-8
find the equation of the line that is parallel to this line and passes through the point (-8,3)

Answers

Answer:

y=9x+75

Step-by-step explanation:

since we know that the slope must be the same for two lines to be proportional, we are gonna start there.

so our equation is: y= 9x + b

we need to find b to complete our equation, so substitute in the points we were given.

3 = 9(-8) + b

so now,

3 = -72 + b

now we have to isolate b to find out what it is,

3 = -72 + b

+72 +72

so now: 75= b

Put that back into the starting equation: y = 9x + 75

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