Identify the Y-intercept
3.5
B
1.5
0.5
2 x
-0.5

Answer:

[tex]x_1=\mathbf{i}\sqrt{6},\ x_2=-\mathbf{i}\sqrt{6},\ x_3=\sqrt{3},\ x_4=-\sqrt{3}[/tex]

Step-by-step explanation:

Biquadratic Equations

Solve:

[tex]x^4 + 3x^2 - 18 = 0[/tex]

The biquadratic equations are equations of degree 4 without the terms of degree 1 and 3.

Solving such equations requires to express the equation as a second-degree equation with [tex]x^2[/tex] as the variable.

Rewriting the equation:

[tex](x^2)^2 + 3(x^2) - 18 = 0[/tex]

The quadratic equation can be factored as:

[tex](x^2+6)(x^2-3)=0[/tex]

It leads to two equations:

[tex]x^2+6=0[/tex]

[tex]x^2-3=0[/tex]

The first equation has imaginary roots. Solving for x:

[tex]x^2=-6[/tex]

[tex]x=\pm\sqrt{-6}[/tex]

[tex]x_1=\mathbf{i}\sqrt{6}[/tex]

[tex]x_2=-\mathbf{i}\sqrt{6}[/tex]

Where

[tex]\mathbf{i}=\sqrt{-1}[/tex]

The second equation has two real roots:

[tex]x^2-3=0[/tex]

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

[tex]x=\pm\sqrt{3}[/tex]

[tex]x_3=\sqrt{3}[/tex]

[tex]x_4=-\sqrt{3}[/tex]

The roots are:

[tex]\mathbf{x_1=\mathbf{i}\sqrt{6},\ x_2=-\mathbf{i}\sqrt{6},\ x_3=\sqrt{3},\ x_4=-\sqrt{3}}[/tex]

Answer:

Solved Examples on Angle of Depression: 1. From the top of a tower, a man finds that the angle of depression of a car on the ground is 30°. If the car is at a distance 40 metres from the tower, find the height of the tower.

Step-by-step explanation:

Answer:

73.2 cm

Step-by-step explanation:

area = 2 bases + 4 sides

area = 2× 3×3 + 4× 3×4.6

area = 2×9 + 4×13.8

area = 18 + 55.2

area = 73.2 cm

Explanation:

For now, ignore the x.

The GCF of 8 and 2 is 2 since 2 is a factor of both

2 = 2*1

8 = 2*4

So if we had 8+2 we can factor 2 out like so to get 2*(4+1)

Notice that I divided each term by 2 when going from 8+2 to 4+1. Then I stuck a 2 outside. You can use the distributive property to check the result.

Similarly,

8x+2 = 2(4x+1)

which you can also check using the distributive property.

Answer:

the answer is C. 60 .....

Answer:

C 60 is the answer

Step-by-step explanation:

75x80 divided by 100= 60

Step-by-step explanation:

y1/x1=y2/x2

2/5÷1/3=y÷1/4

y=3/10=0.3

Answer:

Deena

Step-by-step explanation:

Given:

The perimeter of a triangle is 59 cm.

The first side is 7 cm shorter than the second side.

The third side is 4 cm less than twice the length of the first side.

To find:

The length of each side.

Solution:

Let x be the second side.

Then, according to the question,

First side = x-7

Third side = 2(x-7)-4

Perimeter of a triangle is the sum of all of its sides.

[tex](x-7)+x+(2(x-7)-4)=59[/tex]

[tex]x-7+x+2x-14-4=59[/tex]

[tex]4x-25=59[/tex]

Add 25 on both sides.

[tex]4x=59+25[/tex]

[tex]4x=84[/tex]

Divide both sides by 4.

[tex]x=21[/tex]

Now,

First sides =21 - 7=14 cm

Second side = 21 cm

Third side = 2(14)-4 = 24 cm

Therefore, the three sides of triangle are 14 cm, 21 cm and 24 cm respectively.

Step-by-step explanation:

3x-2x -x = 2-2

x=0

the solutions =2

1) must moves the numbers

2) solve them

Answer:

2 x − y = − 9

Step-by-step explanation:

I am not 100% sure but I think this is right.

Answer:

Step-by-step explanation:

2x+y=9

Answer:

C. It is a whole number that is neither prime nor composite.

Step-by-step explanation:

A prime number is a number that has two factors: one and another number. Thus, since 1 only has one factor (itself), it cannot be a prime number.

However, a composite number must have more than two factors, which 1 doesn't have either.

Since 1 is a whole number (not a decimal or fraction), and it is neither prime nor composite, the answer would be C.

Have a nice day!

Answer:

C!

Step-by-step explanation:

hope it helped

The set of ordered pairs represents a function because every input has only one corresponding output.

Answer:

1&1/8 m/h

Step-by-step explanation:

2/8 of a mile = 1/8 of an hour

add 7/1 to both sides thats 1 and 1/8 of a mile in 1 hour

Answer:

( 0 , 4 )

Step-by-step explanation:

Your estimate is correct

Answer:

(-1, 6)

Step-by-step explanation:

sub the points into the equation if LHS and RHS are equal to each other, it is correct

Lo siento mucho, no hablo muy bien español ... ¡Ojalá pudiera! Sería mucho más útil de esa manera

Answer:

2x^2-5x-12

Step-by-step explanation:

using foil this should be the answer, do you need the solution values?

Answer: she can buy it for 5 friends

Step-by-step explanation:

$35(budget)- $15(craft booth) =$25

then $25 divided by $4 equals 5

So 5 people she can but for.

Answer:

T and Q

Step-by-step explanation:

It is right

Answer:

<STQ and <UTV

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

The final equation is y= -2x+4, so the slope is -2

Answer:

The slope is -2

Step-by-step explanation:

This equation is in point slope form

(y-y1) = m(x-x1)  where m is the slope and ( x1,y1) is a point on the line

y+2=−2(x−3)

y- -2=−2(x−3)

The slope is -2 and a point on the line is ( -3,-2)

Answer: Anthony read 2 pages per minute.

Step-by-step explanation:

Answer: 2 pages/ 1 minute or (2 pages per minute)

Step-by-step explanation: To find the unit rate for how many pages of a book Anthony finds in 23 minutes, you’ll have to divide 46 by 23, which gives you a final result of 2 pages/ 1 minute or (2 pages per minute).

Answer:

C. 3x + 5  = 2x -6

Step-by-step explanation:

it is proportional

cause it is trust me

Answer: it's proportional

Step-by-step explanation:

Answer:

Choice D

Step-by-step explanation:

When you convert a unit to a smaller unit it will always get bigger so in this case you will move the decimal point to the right so 21.5 will become 215.

Answer:

D) 215 millimeters

Step-by-step explanation:

Answer:

y = (x - 6)(x + 1)

Step-by-step explanation:

Use factored form, y = a(x - r1)(x - r2), where r1 and r2 are roots.

Since the solutions are 6 and -1, plug in these numbers:

y = (x - 6)(x + 1)

So, the factored equation is y = (x - 6)(x + 1)

Answer: (x-6)(x+1)

Step-by-step explanation:

Answer:The answer is the option C

Step-by-step explanation:we know that

In a right triangle the Pythagorean Theorem states that

where

c is the hypotenuse (the greater side)

a,b are the legs of the right triangle

in this problem we have

substitute the values

Answer:

15^2 + 16^2= x^2

Step-by-step explanation:

I took the usa test prep test and this is how you calculate it

Answer:

6 Apples

Step-by-step explanation:

There would be six apples and 2 oranges left over.

Hope this Helps!

:D

Answer:

I was kind of confused on this one but is it 15 apples?

Step-by-step explanation:

3, 6, 9, 12, 15

4, 8, 12, 16, 20

I think the answer is 15 apples.

Answer:

5.1

Step-by-step explanation:

To solve this equation I will use the formula a²+b²=c². For these terms I will represent the missing value as the variable a. The equation should be renewed as this: a²+6.4²=8.2², simplified: a²+40.96=67.24. I will now subtract 40.96 from 67.24 to get "a" by itself, as of which now I have a²=26.28. Next I square root both values: √a² =√26.28. The final answer is "a"= 5.1264022471905, otherwise, when rounded, "5.1". Hopefully this helps. A word of advice, when a problem gives you two values for a triangle, always refer to the equation a²+b²=c², as you will always find the missing value. Also remember that the legs cannot be of greater value than the hypotenuse which is the diagonal line. The hypotenuse is always "c".

Answer:

−

2

2

=

2

(

−

1

0

)

x-22={\color{#c92786}{2(x-10)}}

x−22=2(x−10)

−

2

2

=

2

−

2

0

Step-by-step explanation:

Answer:

x=-21

Step-by-step explanation:

first expand the brackets

-22=2x-20

then make x on its own

-42=2x

then dived by 2

-21=x