which is a correct method for solving this equation for X

Answer:

Question 42

area of a triangle = 1/2 × base × height

Given:

Substituting given values into the formula:

⇒ 14 = 1/2 × x × (x + 3)

⇒ 28 = (x + 3)x

⇒ 28 = x² + 3x

⇒ x² + 3x - 28 = 0

⇒ (x - 4)(x + 7) = 0

⇒ x = 4, x = -7

As length is positive, x = 4 only.

⇒ height = 4 + 3 = 7 in

⇒ base = 4 in

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Question 43

volume of a cuboid = length x width x height

Given:

Substituting given values into the formula:

⇒ 72 = 6 × (2x - 5) × x

⇒ 12 = (2x - 5)x

⇒ 12 = 2x² - 5x

⇒ 2x² - 5x - 12 = 0

⇒ (x - 4)(2x + 3) = 0

⇒ x = 4, x = -1.5

As length is positive, x = 4 only.

⇒ height = 4 in

⇒ width = 2(4) - 5 = 3 in

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Question 44

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substituting given values into the formula:

⇒ (x - 7)² + x² = 13²

⇒ x² - 14x + 49 + x² = 169

⇒ 2x² - 14x - 120 = 0

⇒ x² - 7x - 60 = 0

⇒ (x - 12)(x + 5) = 0

⇒ x = 12, x = -5

As length is positive, x = 12 only.

⇒ one leg = 12 m

⇒ other leg = 12 - 7 = 5 m

Using it's concept, it is found that the domain for the expressions is, respectively, given by:

[tex]x \neq 0, x \neq 0, (-\infty, \infty), (-\infty, \infty), x \neq 2[/tex]

It is the set that contains all possible input values.

In a fraction, the denominator cannot be zero, hence:

The third expression can be simplified, as:

(x + 5)/(x + 5) = 1.

The same is true for the fourth, as:

x²/x = 1.

Neither has any restriction, hence their domain is all real numbers, represented by [tex](-\infty, \infty)[/tex].

More can be learned about the domain of a function at https://brainly.com/question/25897115

Answer:

Mode

Step-by-step explanation:

As you can see, the mode on the first data set is 10, the mode on the other is 30.

Answer:

The graph is in the image below

Step-by-step explanation:

you can use an online graphing calculator like Desmos to graph questions like this

I'm not sure if the x2 is x^2 but I will assume

[tex]2x {}^{2} - x - 4[/tex]

[tex]x = \frac{ - ( - 1) + \sqrt{1 - 4(2)( - 4)} }{2(2)} = \frac{1 + \sqrt{33} }{4} [/tex]

[tex]x = \frac{1 - \sqrt{33} }{4} [/tex]

[tex](x - \frac{1 + \sqrt{33} }{4} )(x - \frac{1 - \sqrt{33} }{4} )[/tex]

[tex](4x - 1 - \sqrt{33} )(4x - 1 + \sqrt{33} )[/tex]

18 females, 13 males, total: 31 students.

•female french students: 2

•male french students: 5

probability: male french = 5/31,

total students

edit: as a percentage, 16.129 %

Answer:

10 million

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve for x, you have to isolate it on one side of the equation.

First, subtract by 15 from both sides.

[tex]\sf{5x+15-15=28-15}[/tex]

Solve.

28-15=13

Rewrite the problem down.

5x=13

Divide by 5 from both sides.

[tex]\sf{\dfrac{5x}{5}=\dfrac{13}{5} }[/tex]

Solve.

You can also divide the numbers from left to right.

13/5=2.6

[tex]\boxed{\sf{x=\dfrac{13}{5}=2.6 }}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

[tex]\rightarrow \sf 5x + 15 = 28[/tex]

[tex]\rightarrow \sf 5x + 15 -15= 28-15[/tex]

[tex]\rightarrow \sf 5x = 13[/tex]

[tex]\rightarrow \sf \dfrac{5x}{5} = \dfrac{13}{5}[/tex]

[tex]\rightarrow \sf x = \dfrac{13}{5}[/tex]

[tex]\rightarrow \sf x = 2\dfrac{3}{5}[/tex]

[tex]\rightarrow \sf x = 2.6[/tex]

Answer:

Angle A=87°

Step-by-step explanation:

(5x-3)°+(4x+21)°=180°

9x°+18°=180°

9x°+18°-18°=180°-18°

9x°=162°

9x°/9°=162°/9°

x=18°

Angle A=(5x18-3)°

(90-3)°

Angle A=87°

Answer:

0.65 is a number greater than 0.6 but less than 0.7

Answer:

True

Determine whether x+2 is a factor of x³-3x²-7x+6:

↓

[tex]True[/tex]

I hope this helps you

:)

Answer:

Step-by-step explanation:

Answer:

1 yard = 3 feet: 3.25 yards x 3 feet per yard = 9.75 feet. 1 foot = 12 inches: 9.75 feet x 12 inches per foot = 117 inches.

Step-by-step explanation:

1 yard = 3 feet: 3.25 yards x 3 feet per yard = 9.75 feet. 1 foot = 12 inches: 9.75 feet x 12 inches per foot = 117 inches.

it's a cubic function

The given function f(x) = 2x³ – 4x² + 5 is a cubic function.

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

A cubic polynomial is a sort of polynomial that is based on the variable's largest exponent, or degree, in mathematical terms. As a result, a cubic polynomial is one in which the degree or maximum power of the variable is 3.

It is observed that the given function is a cubic function as its highest power of the variable is three.

Therefore, the given function f(x) = 2x³ – 4x² + 5 is a cubic function.

To know more about cubic polynomials follow

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Answer:

Step-by-step explanation:

c

Answer:

y+4

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Let's say we have y=f (x)

It denotes the y value that corresponds to x.

When x=3, we can see from the graph that

The matching y value for x=3 =1

As a result, h(3)=1

The value of h(3) can be estimated from the piecewise function curve is 1. so option c is correct.

A function that is composed of several smaller functions, each with a distinct domain, is said to be piecewise. The term "piecewise" refers to the way in which these sub-functions are defined in terms of various intervals or "pieces" of the function's overall domain.

Given that,

The graph of the piecewise function

The function is divided into two piece

Interval-1     x ∈ [-4, -1)

Interval-2   x ∈  [-1, 4]

The value of the function when x  is equal to 3,

In the graph it is clearly mention that for x =3

the output value of the function is 1

Hence, the output value is 1

To know more about piecewise function check:

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Answer:

47

Step-by-step explanation:

10z + 4 + 8z + 2 = 168

first we find z

z = 9

5×9 +2 is 47

ANSWER IS 47

Mary is wrong because ∠A = ∠B = 63°, while ∠C = x ≠ 63°

A triangle is a polygon with three sides and three angles. Types of triangles are equilateral, isosceles and right angled.

An isosceles triangle is a triangle in which two sides and two angles are equal.

From the diagram:

∠A = ∠B (base angles)

Mary is wrong because ∠A = ∠B = 63°, while ∠C = x ≠ 63°

Find out more on triangle at: https://brainly.com/question/17335144

Lets let Teddy be x.

Sister 1: x+3

Sister 2: x-7

If we subtract the younger sister (sister 2) from the older sister (sister 1), we get:

x+3 - (x-7) = x+3 - x + 7 = 10

The older sister was 10 years old when the younger sister was born.

Answer:

x= -28

Step-by-step explanation:

1. First you have to add 14 to both sides to get the x by itself. That's always the first thing you have to do. Get x by itself.

2. After that, you should have -x= 28. You can't leave it like that because it is still not simplified. It's basically saying 28 is the opposite of x. What's the opposite of positive? Negative.

3. Therefore, your final answer should be -28

Answer:

x = -28

Step-by-step explanation:

Hey! First, lets establish our equation :)

-14 -x = 14

Now, we are going to get our x alone on a single side, to do this, we are going to add 14 to both sides to be able to cut out -14 on the left side!

-14 -x = 14

+14      +14

     -x = 28

The last thing we have to do is divide both sides by -1 to get x by itself without it being negative!

-x = 28

÷-1  ÷-1

x = -28

So, x, is equal to -28 (negative 28!) :)

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

5.5 and 6

Step-by-step explanation:

i got it wrong and it told me this was the correct answer

Answer:

5.5 and 6

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

Domain = [-7,4]

Range = [-4,8]

Step-by-step explanation:

Domain= all values of x

Range= all values of y

becuase there are no values going to infinity and they all end, we can just look at our end points.

Answer:

D

Step-by-step explanation:

[tex]4\sqrt{x2[/tex] means [tex](x^{2})^{\frac{1}{4} }[/tex] so then according to indices rule, the powers will be multiplied. Do the same thing for y and z as well, and you will get the answer

Answer:

x=23

Step-by-step explanation:

An inscribed angle is half of the intercepted arc.

Answer:

2.5, which would be 2:30 hours

Step-by-step explanation:

time/distance:

22.5/9 = 2.5

9 x 2.5 = 22.5

so the answer is 2.5

Answer:

2.5 hours

Step-by-step explanation:

[tex]\sf time \ taken = \dfrac{distance}{speed}[/tex]

Here:

[tex]\hookrightarrow \sf \dfrac{22.5}{9}[/tex]

[tex]\hookrightarrow \sf 2.5[/tex]

If A:B = 7:8 an B:C =12:7,find