how to find rationalizing factor of

class 9​

The U shape is called a parabola

If the "a" is positive, then the parabola opens upward as shown in the graph on the left.

If "a" is negative, then the parabola opens downward. This is the parabola on the right.

The way I remember is that "a" being positive means it puts a smile on, which is what the parabola on the left resembles. The parabola on the right is a frowny face so "a" is negative.

A parabola is vertically cut in half by the axis of symmetry. One half mirrors over this vertical line to get the other half. The axis of symmetry passes through the vertex. The vertex is either the highest point or the lowest point depending on whether 'a' is negative or positive.

Answer:

E. - 7

Step-by-step explanation:

2x2-X2+5X-10-4=0

X2+5X-14=0

X2-2X+7X-14.=0

X(X-2). 7(X-2)=0

(X+7). (X-2)

X=-7, X=2

Answer:

the answer is -7 and 2

Step-by-step explanation:

Answer:

2x/3 - 5 = 21

2x/3 = 26

2x = 78

x = 39

Step-by-step explanation:

Answer:

x = 39

Step-by-step explanation:

Answer:ok

Step-by-step explanation:wow

Answer:

y = ½x + ¾

slope (m) = ½

y-intercept(b) = ¾

Step-by-step explanation:

4y - 2x = 3

4y = 2x + 3

y = (2x + 3) ÷ 4

y = 2/4x + 3/4

y = ½x + ¾

slope (m) = ½

y-intercept(b) = ¾

Answer:

2+2y

Step-by-step explanation:

20=2(y-6)+10

20= (2×y-2×6)+10

20= (2y-12)+10

Open the bracket

20=2y-12+10

Collect liked terms

20=12+10+2y

20=22+2y

=22-20+2y

2+2y

Hope this helps

Comment for more explanation

Answer:

Option two and three for the domain and range question

Answer: (0.8115, 0.8645)

Step-by-step explanation:

Let p be the proportion of people who leave one space after a period.

Given:  Sample size : n= 525

Number of people responded that they leave one space. =440

i.e. sample proportion: [tex]\hat{p}=\dfrac{440}{525}\approx0.838[/tex]

z-score for 90% confidence level : 1.645

Formula to find the confidence interval :

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

[tex]0.838\pm (1.645)\sqrt{\dfrac{0.838(1-0.838)}{525}}\\\\=0.838\pm (1.645)\sqrt{0.00025858285}\\\\=0.838\pm (1.645)(0.01608)\\\\= 0.838\pm0.0265\\\\=(0.838-0.0265,\ 0.838+0.0265)\\\\=(0.8115,\ 0.8645)[/tex]

Hence, a 90% confidence interval for the proportion of people who leave one space after a period: (0.8115, 0.8645)

Answer:

7√2

Step-by-step explanation:

Knowing that the angle is 45° (or π/4 radians) and the opposite leg has a length of 7,  you can find the length of b with:

7 / b = sin(π / 4)

7 / (sin(π / 4)) = b

b = 7 / (1 / √2)

b =7√2

A simpler way to get the answer is to note that a right triangle with one 45° angle must be an isoceles right triangle, so both legs are the same length. Using the Pythagorean Theorem:

a² + 7² = b²

Since we know a = 7,

7² + 7² = b²

b = √(2 * 49)

b = 7√2

Answer:

"statement 1: The number of boys at the school is [tex]\frac{4}5[/tex] of the number of girls." is true.

Step-by-step explanation:

Given:

Ratio of Number of boys to the number of girls = 4 : 5

Total number of students = 270

To find:

Number of boys in terms of number of girls = ?

Solution:

As per given statement,

Let, Number of boys = [tex]4x[/tex]

Let, Number of girls = [tex]5x[/tex]

Total number of students = Number of boys + Number of girls = 270

[tex]\Rightarrow 4x+5x =270\\\Rightarrow 9x=270\\\Rightarrow \bold{x = 30}[/tex]

Therefore, number of boys = 4 [tex]\times[/tex] 30 = 120

And, number of girls = 5 [tex]\times[/tex] 30 = 150

As per Statement 1:

Finding [tex]\frac{4}5[/tex] of the number of girls:

[tex]\dfrac{4}{5}\times 150 = 4 \times 30 = 120[/tex] = Number of boys.

Finding [tex]\frac{4}9[/tex] of the total number of students:

[tex]\frac{4}{9}\times 270= 4 \times 30 = 120[/tex] = Number of boys.

Number of boys is equal to [tex]\frac{4}9[/tex] of total number of students.

So, "statement 1: The number of boys at the school is [tex]\frac{4}5[/tex] of the number of girls." is true.

Answer:

x=8

Step-by-step explanation:

3x -5 =2.5x + 3 - (x-4)

3x - 5 = 2.5x + 3 -x+4

3x - 5 = 1.5x +7

1.5x = 12

x =8

The solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

The given expression is,

x-5=2.5x+3-(x-4)

Simplify the equation by combining like terms.

Start with the terms on the right-hand side of the equation:

2.5x+3-(x-4)

= 2.5x + 3 - x + 4 (distributing the negative sign)

= 1.5x + 7

Now let's combine the terms on the left-hand side of the equation:

3x - 5

Now the reduced equation be,

3x - 5 = 1.5x + 7

Isolate the variable (x) on one side of the equation.

Subtracting 1.5x from both sides:

3x - 1.5x - 5 = 1.5x - 1.5x + 7

1.5x - 5 = 7

Add 5 to both sides:

1.5x - 5 + 5 = 7 + 5

1.5x = 12

Solve for x by dividing both sides by 1.5:

1.5x/1.5 = 12/1.5

x = 8

So the solution to the linear equation 3x - 5 = 2.5x + 3 - (x-4) is x = 8.

To learn more about equations visit:

https://brainly.com/question/29174899

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Answer:

B. No solutions

Step-by-step explanation:

8x+2y=14

8x+2y=4

These linear equations are in standard form, and the Ax values are the same (8x) and the By values are the same (2y).  The only value that is the different is the C values (14 and 4), which will be the cause of a no solution for this system of equations.

Answer:

b

..........

Step-by-step explanation:

0≠14-4

...

Answer:

x = 1

y = 5

Step-by-step explanation:

5x - 2y = -5

5x + 6y = 35

=> 5x + 6y = 35

=> 5x - 5x + 6y = 35 - 5x

=> 6y = 35 - 5x

=> 6y/6 = 35/6 - 5/6x

=> y = 35/6 - 5/6x

=> 5x - 2 (35/6 - 5/6x) = -5

=> 5x - 35/3 + 5/3x = -5

=> 15/3x -35/3 + 5/3 = -15/3

=> 20/3x -35/3 = -15/3

=> 20/3x -35/3 + 35/3 = -15/3 + 35/3

=> 20/3x = 20/3

=> 20/3x * 3 = 20/3 * 3

=> 20x = 20

=> 20x/20 = 20/20

=> x = 1

=> 5x + 6y = 35

=> 5(1) + 6y = 35

=> 5 + 6y = 35

=> 5 -5 + 6y = 35 -5

=> 6y = 30

=> 6y/6 = 30/6

=> y = 5

So, x = 1

     y = 5

Answer:

Step-by-step explanation:

That will be 3a + 3b + 3c pounds of mortar.

as there will be 3a pounds of water and 3c pounds of cement.

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Work Shown:

Straight lines DF and EC intersect at point A. Because of this, angle DAF is a 180 degree angle.

Angles DAB, BAC, and CAF all combine to form a straight 180 degree angle.

Add up the angles mentioned, set the sum equal to 180, and solve for x

-----------

(angle DAB) + (angle BAC) + (angle CAF) = 180

x + 80 + 60 = 180

x + 140 = 180

x + 140-140 = 180-140 ... subtract 140 from both sides

x = 40

Answer:

[tex]\Huge \boxed{x=40\°}[/tex]

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

We can create an equation and solve for x.

x + 80 + 60 = 180

Add the numbers on the left side.

x + 140 = 180

Subtract 140 from both sides.

x + 140 - 140 = 180 - 140

x = 40

Step-by-step explanation: lol like a dozen

it is a number less then zero

Answer:

a negative number is when a number exceeds below zero

for example 7 --8 would be -1

Answer:

Step-by-step explanation:

-5+1

-4

Answer:

89 , 91

Step-by-step explanation:

let one be x and the other be x+2

Supplementary angles are those angles that sum up to [tex]180^{o}[/tex]

equating both sides

x+x+2 = 180

2x+2 = 180

2x = 180-2

2x = 178

x = 89

x+2 = 89+2 = 91

Answer:

its a.

Step-by-step explanation:

Answer:  see proof below

Step-by-step explanation:

Use the following Product to Sum Identities:

2 sin A sin B = cos (A - B) - cos (A + B)

2 sin A cos B = sin (A + B) + sin (A - B)

Use the Unit Circle to evaluate: cos 120 = -1/2    &      sin 60 = √3/2

Proof LHS → RHS

LHS:                                            sin 20 · sin 40 · sin 80

Regroup:                              (1/2) sin 20 · 2 sin 40 · sin 80

Product to Sum Identity:     (1/2) sin 20 [cos(80-40) - cos (80+40)]

Simplify:                                (1/2) sin 20 [cos 40 - cos 120]

Unit Circle:                            (1/2) sin 20 [cos 40 + (1/2)]

Distribute:                             (1/2) sin 20 cos 40 + (1/4) sin 20

Product to Sum Identity:       (1/4)[sin(20 + 40) + sin (20 - 40)] + (1/4) sin 20

Simplify:                                 (1/4)[sin 60 + sin (-20)] + (1/4) sin 20

                                           = (1/4)[sin 60 - sin 20] + (1/4) sin 20

Unit Circle:                             (1/4)[(√3/2) - sin 20] + (1/4) sin 20

Distribute:                              (√3/8) -  (1/4) sin 20 + (1/4) sin 20

Simplify:                                  √3/8

LHS = RHS:   √3/8 = √3/8  [tex]\checkmark[/tex]

We are given the equation cos(20°)(cos(40°)(cos(60°)(cos(80°) = √3 / 8. Let's once again start by applying the identity 'sin(s)sin(t) = - cos(s + t) + cos(s - t) / 2. In this case if we focus on the expression 'cos(20°)(cos(40°),' s would be = 20°, and t = 40°.

[tex]\mathrm{Use\:the\:following\:identity}:\quad \sin \left(s\right)\sin \left(t\right)=\frac{-\cos \left(s+t\right)+\cos \left(s-t\right)}{2}[/tex]

[tex]\sin \left(20^{\circ \:}\right)\sin \left(40^{\circ \:}\right)=\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}[/tex]

[tex]\mathrm{Substitute}:\frac{-\cos \left(20^{\circ \:}+40^{\circ \:}\right)+\cos \left(20^{\circ \:}-40^{\circ \:}\right)}{2}\sin \left(80^{\circ \:}\right)[/tex]

[tex]\mathrm{Multiply\:fractions}:\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(-20^{\circ \:}\right)\right)}{2}[/tex]

Remember that cos(- x) = cos(x). Respectively cos(- 20°) = cos(20°). Let's substitute and afterwards apply the identity 'cos(60°) = 1 / 2.'

[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-\cos \left(60^{\circ \:}\right)+\cos \left(20^{\circ \:}\right)\right)}{2} = \frac{\sin \left(80^{\circ \:}\right)\left(-\frac{1}{2}+\cos \left(20^{\circ \:}\right)\right)}{2}[/tex]

And if we further simplify the expression, we should receive the following...

[tex]\frac{\sin \left(80^{\circ \:}\right)\left(-1+2\cos \left(20^{\circ \:}\right)\right)}{4}[/tex]

Now we want to prove that this expression = √3 / 8. The denominator here is 4 so we can multiply the whole thing by 2 to have a denominator of 8. 2((sin(80°)(- 1 + 2cos(20°)) when simplified = √3. Therefore the expression is true.

Data:

age of Dollah = x (unknown element)

age of Fatimeh = x + 5 (age of Dollah + 5)

the product is 234

Equation:

x * (x + 5) = 234

x² + 5x = 234

x² + 5x - 234 = 0

Δ = b² - 4 a c = 5² - 4 (1 * -234) = 25 - 4 (-234) = 25 - (-936)

= 25 + 936 = 961

x₁,₂=[tex]\frac{b^{2} ± \sqrt{delta} }{2a}[/tex] = [tex]\frac{5^2 +/- \sqrt{961} }{2}[/tex] = [tex]\frac{25 +/- 31}{2}[/tex]

x1 = (25+31)/2 =  56 / 2 = 28

x2 = (25 -31)/2 = -6 / 2 = -3 [age can't be negative, so the first one is accettable]

So:

Dollah's age (x) = 28 years old

Fatima's age (x + 5) = 28 + 5 = 32 years old

Answer:

4

Step-by-step explanation:

- and - become +

so, -12 + 8 = -4

but we remove the minus and make it a positive 4

Answer:

28

Step-by-step explanation:

The first five prime numbers are = 2,3,5,7,11

Addition of the prime nos. = 2+3+5+7+11=28

The first prime numbers are: 2, 3, 5, 7, 11.

The sum is 2 + 3 + 5 + 7 + 11 = 28, so option 4

Answer:

DIVISION PROPERTY OF EQUALITY

Step-by-step explanation:

Given the equation r4 = 16,wm we can rewrite the equation as 4r = 16

The coefficient at the left hand side of the equation that we are to move to rge right is 4 (the number attached to the r variable). To do this we are going to apply the Division property of equality. This property is a property where both sides of an equation is divided through by the same constant without affecting the equality sign or by still keeping the equation.

To move the coefficient of r to the other side, we will divide both sides of the equation by 4 as shown;

4r/4 = 16/4

r = 4×4/4

r = 4

Hence the property that is used to move the coefficient (4) to the other side of the equation is the DIVISION PROPERTY OF EQUALITY.

Answer:

24

Step-by-step explanation:

The answer to the question is 46

Answer:

x=2

Step-by-step explanation:

1+4x=7+x

↦4x-x=7-1

↦3x=6

↦x=6/3

↦x=2

.°. x=2

Hope you understand it

Answer:

x = 2

Step-by-step explanation:

For this equation, we simply need to solve for x.

1 + 4x = 7 + x

1 + -1 + 4x = 7 + -1 + x

4x = 6 + x

4x + -x = 6 + x + -x

3x = 6

3x * (1/3) = 6 * (1/3)

x = 2

So the solution to this equation is x = 2.

Cheers.

Answer:

4/6 and 8/12 and 16/24

Step-by-step explanation:

well because it is math and math works like this basically all of theese are equal to 2/3

Answer:

6 ducks

Step-by-step explanation:

Monday, Brian counted 28 ducks and Cathy counted 15 ducks

                = 28+15 =43

Tuesday, they counted 37

Monday count - Tuesday count

43 - 37 =6