5(2x - 12) + 21 = 2x + 41
05
08
O 10
072

Answer:

x = 10

Step-by-step explanation:

the ray is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides , that is

[tex]\frac{x+4}{2x +1}[/tex] = [tex]\frac{8}{12}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

2(2x + 1) = 3(x + 4) ← distribute parenthesis

4x + 2 = 3x + 12 ( subtract 3x from both sides )

x + 2 = 12 ( subtract 2 from both sides )

x = 10

Answer:

09

Step-by-step explanation:

34

Answer:

x = 1 or x = -1

Step-by-step explanation:

Given equation:

[tex]x^{100}-4^x \cdot x^{98}-x^2+4^x=0[/tex]

Factor out -1:

[tex]\implies -1(-x^{100}+4^x \cdot x^{98}+x^2-4^x)=0[/tex]

Divide both sides by -1:

[tex]\implies -x^{100}+4^x \cdot x^{98}+x^2-4^x=0[/tex]

Rearrange the terms:

[tex]\implies 4^x \cdot x^{98}-4^x-x^{100}+x^2=0[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c \quad \textsf{to }x^{100}:[/tex]

[tex]\implies 4^x \cdot x^{98}-4^x-x^{98}x^2+x^2=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 4^x(x^{98}-1)-x^2(x^{98}-1)=0[/tex]

Factor out the common term [tex](x^{98}-1)[/tex] :

[tex]\implies (4^x-x^2)(x^{98}-1)=0[/tex]

Zero Product Property:  If a ⋅ b = 0 then either a = 0 or b = 0 (or both).

Using the Zero Product Property, set each factor equal to zero and solve for x (if possible):

[tex]\begin{aligned}x^{98}-1 & = 0 & \quad \textsf{or} \quad \quad4^x-x^2 & = 0 \\x^{98} & =1 & 4^x & = x^2 \\x & = 1, -1 & \textsf{no}& \textsf{ solutions for } x \in \mathbb{R}\end{aligned}[/tex]

Therefore, the solutions to the given equation are: x = 1 or x = -1

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The Answer is in simplest form:-

4/9

=0.4444444444

Answer:

4/9

Step-by-step explanation:

1) since we know that; when a fraction is raised to a negative power, we take reciprocal of the fraction and raise both the numerator and the denominator to a positive power,

(27/8)^-⅔

that's how we write it then

2) we take the reciprocal and multiply with positive power respectively

(8/27)⅔

that is by expanding

8^⅔/27^⅔

enter it in your calculator and you should get

4/9

hope that helps!

Answer:

113 degrees

Step-by-step explanation:

Two angles are called supplementary when they add up to 180 degrees

[tex]180 = x + y \\ 180 = 67 + y \\ y = 180 - 67 \\ y = 113 \\ therefore \: mB \: = 113[/tex]

The value of TY is 14

Given that CD is the perpendicular bisector of XY and ST and CY = 16

We need to find the value of TY

Here M is the midpoint of ST  and D is the midpoint of XY

As shown in the diagram we can say that

CT = CS =12

We can also say that ST║XY

So , ∠CST = ∠CSY

∠CTS = ∠CYX

ΔSCT = ΔXCY

SX = CS - CX

= CY - CX

We can say that MT = SM = 5

DY = DX = 7

TY = SX = 4

CY = CX = 16

ST = SM + MT

ST= 5+5

∴ ST= 10

XY = XD +DY

XY = 7+7

∴ XY = 14

Hence the value of XY is 14

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The linear inequality  [tex]y \leq 5/2(x + 2)[/tex] will not have a shared solution set with the graphed linear inequality. the correct option is D.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

On a coordinate plane, a solid straight line has a negative slope and goes through (-2, 2) and (2, -8).

m = (-8 -2)/ (2 +2)

m = -10/ 4

m = -5/2

The line has an equation of y greater-than-or-equal-to negative five-halves x minus 3.

[tex]y \geq -5/2 (x-3)[/tex]

The linear inequality  [tex]y \leq 5/2(x + 2)[/tex] will not have a shared solution set with the graphed linear inequality.

Thus, the correct option is D.

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Answer:

its b the guy above me is wrong

Step-by-step explanation:

Step-by-step explanation:

I have done it go and check it once

Answer:

[tex]\huge\boxed{\dfrac{6}{10}=0.6}[/tex]

Step-by-step explanation:

[tex]0.6=\dfrac{6}{10}[/tex]

one digit after the decimal point - one zero in the denominator

[tex]0.06=\dfrac{6}{100}[/tex]

two digits after the decimal point - two zeros in the denominator

[tex]6.0=6[/tex]

[tex]1.6=1\dfrac{6}{10}\ \text{or}\ 1.6=\dfrac{16}{10}[/tex]

Answer:

Correct expression:

[tex]2x + 3y + 25[/tex]

Answer:

y = 2

Step-by-step explanation:

Y varies indirectly with x (as x gets bigger, y gets smaller)

You have to find k, the constant of proportionality.

y = [tex]\frac{k}{x}[/tex]

Plus in the x & y values you are given

58 = [tex]\frac{k}{9}[/tex]  Multiply both sides by 9 to solve for k

k= 522

Now plug in the new value of x to solve for y

y = [tex]\frac{522}{261}[/tex]

y = 2

After doing simplification, the result that we got is the quadratic formula

x = [-b ±√(b² - 4ac)] / 2a.

The given statement can be explained with the following equation:

[x + (b/2a)]² = (b² - 4ac) / 4a²

Now, we will take the root on both the sides:

x + (b/2a) = ±√[(b² - 4ac) / 4a²]

x = -(b/2a) ± √[(b² - 4ac) / 4a²]

x = [-b ±√(b² - 4ac)] / 2a

The final equation resembles the quadratic formula.

So, the result of applying the square root property to this equation is that we get the quadratic formula after simplification.

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Answer:

The correct set of equations is C.

Step-by-step explanation:

m + n = 32

m = 3n

We have 4n = 32, so n = 8 and m = 24.

The area of ABCD is 104 units²

The area of rectangle is the product of its length to its breadth.

i.e., Area of rectangle= length * breadth

As, ABCD is in the shape of rectangle.

Using distance formula,

AB = √(1-(-5)² + (6-2)²

AB = √36+16

AB = √52

AB= 2√13

BC= √(9-1)² + (-6-6)²

BC= √64+144

BC =√208

BC= 4√13

Now, area of rectangle

=length *  breadth

= 2√13 * 4√13

= 8*13

=104  units²

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[tex]3x ^{2} \: + \: {6x}^{3} \: - \: 9 {x}^{2} y[/tex]

[tex] \boxed{ \bold{3 {x}^{2} \: \times \: (1 \: + \: 2x \: - \: 3y)}}[/tex]

Answer:

[tex]\boxed{3x²(1 + 2x - 3y)}[/tex]

Step-by-step explanation:

3x squared + 6 x cube - 9x squared y

To factor

Solution:

A process when algebraic expression is expressed as a product of two or more expressions is factorisation.

ATP,

Square = a²

Cube = a³

We can see that 3x^2 is common in this expression.

So rewrite as:

Done!

The height of the tree is the man's height plus x.

[tex]\tan 26^{\circ}=\frac{x}{16}\\x = 16 \tan 26^{\circ}[/tex]

So, the height of the tree is [tex]\boxed{(16 \tan 26^{\circ}+1.8) \text{ m}}[/tex]

To find the equation of a parabola given the vertex and the zeroes, we can use the intercept form equation to help us:

[tex]y=a(x-r)(x-s)[/tex]

We're given:

[tex]y=a(x-r)(x-s)[/tex]

⇒ Plug in the given information:

[tex]y=a(x-(-8))(x-4)\\18=a(-2-(-8))(-2-4)\\18=a(-2+8)(-2-4)\\18=a(6)(-6)\\18=a(-36)\\1=-2a\\\\a=-\dfrac{1}{2}[/tex]

[tex]a=-\dfrac{1}{2}[/tex]

Answer:

21.5

Step-by-step explanation:

break the shape down to make two shapes: a triangle and rectangle.
triangle = A=bxh/2

3x5=15/2=7.5

Rectangle = A=bxh

2x7=14

7.5+14= 21.5

Hope this helps :)

Answer:

21.5

Step-by-step explanation:

(all steps provided in image attached)

Answer:

Acute, right angle, obtuse, reflex

Step-by-step explanation:

Answer:

Acute

right angle

obtuse

reflex angle

Step-by-step explanation:

Answer:

11 and 22

Step-by-step explanation:

let one positive integer be n then the other is 2n , so

n × 2n = 242

2n² = 242 ( divide both sides by 2 )

n² = 121 ( take square root of both sides )

n = [tex]\sqrt{121}[/tex] = 11

2n = 2 × 11 = 22

the 2 integers are 11 and 22

A will have a value of 2. The value of A is found by the substitutional equation system.

A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.

The given equation in the problem is;

Equation 1: [tex]\rm \frac{3}{8} + \frac{1}{3} y= \frac{17}{24}[/tex]

Equation 2: [tex]x+7y=8[/tex]

Rearrange equation 2 as;

x=8-7y

Substitute the value of x;

[tex]\rm \frac{3}{8} + \frac{1}{3} y= \frac{17}{24} \\\\ \frac{3}{8}(8-7y)+\frac{1}{3}y=\frac{17}{24} \\\\ \frac{-21}{8} y+\frac{1}{3} = \frac{17}{24}-3 \\\\ \frac{-63y+8y}{24}=\frac{17-72}{24}\\\\ \frac{-55 \ y}{24} = - \frac{55}{24}\\\\ y= 1[/tex]

Substitute the value of y in equation 2 as;

x+7y=8

x+7(1)+8

x=8-7

x=1

The system of equations by substitution obtained the value of A is;

x + y = A

1+1=A

A=2

Hence the value of A will be 2.

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Answer:

The factors are (x-7) and (x-4)

Step-by-step explanation:

We are finding the factors of a function from the zeros

The zeros are 7 and 4

We can use the zero product property which is

(x-b)(x-c) = 0  where b and c are the zeros

(x-7) (x-4) =0

The factors are (x-7) and (x-4)

See below for the verification of ∠ACD =  ∠ABC + ∠BAC

The following proof works for both triangles.

The sum of angles in a triangle is 180 degrees.

So, we have:

∠ABC + ∠BAC + ∠ACB = 180

Make ∠ACB the subject

∠ACB = 180 - ∠ABC - ∠BAC

The sum of angles on a straight line is 180 degrees.

So, we have:

∠ACD + ∠ACB = 180

Make ∠ACB the subject

∠ACB = 180 - ∠ACD

Substitute ∠ACB = 180 - ∠ACD in ∠ACB = 180 - ∠ABC - ∠BAC

180 - ∠ACD = 180 - ∠ABC - ∠BAC

Subtract 180 from both sides

- ∠ACD = - ∠ABC - ∠BAC

Multiply both sides by -1

∠ACD =  ∠ABC + ∠BAC

Hence, ∠ACD =  ∠ABC + ∠BAC has been verified

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The third side is a linear expression , Option A is the right answer.

The missing diagram is attached with the figure.

A triangle is a polygon with three sides , three vertices , three angles .

It is given that the side of the triangle as 3x+1 , 5x-2 , y

Perimeter is given as 10x-1

Perimeter = 3x+1 +5x-2 + y  = 10x-1

8x -1 +y = 10x -1

y = 2x

which is a linear expression.

Therefore the third side is a linear expression , Option A is the right answer.

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Answer:

2. All reals

Step-by-step explanation:

It covers everything as absolute value (distance from 0)

If you graph it you will see

Reason:

Absolute value represents distance on a number line. Specifically it's the distance from x to 0.

For example, |-2| = 2 means -2 is 2 units away from 0.

Since |x| represents a distance, we cannot have negative distance. So |x| is either 0 or positive. Furthermore, it means |x| is larger than any negative value you pick.

Therefore, |x| > -9 is true for any x value and it's why we go for "all reals" (aka "all real numbers")

Answer:

-14/15

Step-by-step explanation:

"of" means multiply, thus:

-8/15 * 21/12

-8 * 21 / 15 * 12

-2 * 7 / 15

-14/15

Answer:

-14/15

Step-by-step explanation:

So first you need to get rid of the negative sign. Don't worry you will add it back later!

So, you will do

-8/15×21/12

Once you cross cancel, you will have

-2/5x7/3

That would be equivalent to

-14/15

That's your answer!

Hope this helped :)

Answer:

congruent/alternate interior angles

Step-by-step explanation:

just took the quiz

The area of the kite ABCD will be 60 square millimeters.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

In the Kite ABCD, AB = 5√2mm = 7.07 mm, AP= 5mm, PD = 7mm

Then the area of the kite ABCD will be

Area = 2(area of triangle APB and area of triangle APD)

The side length of PB will be

AB² = AP² + PB²

PB² = AB² – AP²

PB² = 7.07² – 5²

PB² = 50 – 25

PB² = 25

 PB = 5 mm

Then the area will be

Area = 2[(1/2 × 7 × 5) + (1/2 × 5 × 5)]

Area = 60 square mm

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