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Answer:

x = 4

Step-by-step explanation:

Use order of operations (PEMDAS) to simplify and solve algebraic equations:

P - Parentheses: Simplify all parentheses in the equation first.
E - Exponents: Evaluate all exponential expressions in the equation next.
M/D - Multiplication/Division: After P and E, Multiplication in the equation comes next. These are interchangeable, so if these are the only operations left, calculate in the direction left to right.
A/S - Addition/Subtraction: After everything else has been done, move on to Addition/Subtraction.  These two are also interchangeable, so you must also calculate in the direction left to right.

First, implement the order of operations to simplify the equation:

2²(x + 3) + 9 - 5 = 32 --- Evaluate the exponent.

4(x + 3) + 9 - 5 = 32 --- Use the Distributive Property to multiply.

4x + 12 + 9 - 5 = 32 --- Add/Subtract (Combine like terms).

4x + 16 = 32

Next, isolate the variable x to solve for its value:

4x + 16 = 32 --- Subtract 16 from both sides of the equation.

4x = 16 --- Divide both sides of the equation by 4 to get the value of x.

x = 4

To confirm that x = 4, you can substitute x for 4 in the original equation and see if both sides of the equation are equal:

2²[(4) + 3] + 9 - 5 = 32 --- Simplify the parentheses.

2²(7) + 9 - 5 = 32 --- Evaluate the exponent.

4(7) + 9 - 5 = 32 --- Multiply.

28 + 9 - 5 = 32 --- Simplify the equation using Addition/Subtraction.

32 = 32

After using substitution, we can confirm that x = 4.

To solve for the x-variable in a linear equation, we will need to isolate it on one side of the equation. If the x-variable is inside a parenthesis, we will need to open the parenthesis first, then isolate the variable. To solve/simplify the equation, we will need to use PEMDAS. It is a common method used to simplify equations and inequalities through priorities.

The word "PEMDAS" is a shortened word of "Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction". We follow this order (left-right) to simplify algebraic terms. Since parenthesis is the first priority, we would simplify the expression inside the parentheses. There are two exceptions to this priority in PEMDAS. (1) One of the terms in the expression is a variable, so the expression cannot be simplified, or (2) if there was no parenthesis in the first place. The next priority is "Exponents". This priority is used if there are any exponents used in the equation. The only exception to this priority is when there are no exponents used in the equation. The next priority is "Multiplication". This means that you have to simplify any products "multiplying terms" first. The only exception to this is when there are no terms being multiplied. The next priority is "Division". This priority tells that we need to simplify any division occurring the equation next. There is only one exception to this priority. Only possible if there is no division occurring in the equation. Then, we have "addition" as our 5th priority. This priority states that simplifying any expression that is being added next. The only exception to this priority is when there are no terms being added. The last and final priority is subtraction. This priority states that simplify any expression that is being subtracted. There is no exception to this priority.

Simplifying the equation using PEMDAS:

We have the following equation: 2²(x + 3) + 9 - 5 = 32

Let us simplify using our first priority. Unfortunately, there is a variable inside the parenthesis. Therefore, we can't simplify the expression inside the parenthesis. Let us now simplify using out second priority. We can see a term outside the parenthesis "2²". Since that term has an exponent, let us simplify that term! Eventually, the term will simplify to 4.

Before we move onto the next priority, let us open the parenthesis as we need to isolate the x-variable. This basically means that we need to simplify the distributive property. To simplify the distributive property, we need to multiply the term outside the parenthesis to all the terms inside the parenthesis. So, we have the following simplified equation:

Our next priority is multiplication. So, let us simplify any products occurring in the equation. We can see 4 being multiplied to 3. Therefore, let us simplify that term! Simplifying that term basically gives us 12. So:

Now, our next priority is division. However, we do not see any division occurring in the equation. Therefore, this follows the exception of the division priority in PEMDAS. So, let us move on to the next priority.

The next priority is addition. We can see 12 being added to 9. Therefore, let us simplify the expression. Simplifying that expression gives us 21. So:

The last and final priority is subtraction. We can see 5 being subtracted from 21. Therefore, let us simplify the expression, which gives us 16. So:

Solving for the x-variable by isolating it:

Now, let us isolate the x-variable to determine its value. This can be done by subtracting 16 on both sides of the equation. Then, we can divide 4 both sides to cancel out the coefficient of x.

Therefore, the value of x in the equation is 4.

The number of cows and ducks in the garden are 3 and 4 respectively.

Let the numbers of cows be x and the number of ducks is y.

Total number of legs=20

Total number of eyes=14

Linear equation for the total number of legs in the garden,

4x+2y=20 -(1)

Linear equation for the total number of eyes in the garden,

2x+2y=14 -(2)

Solve the system of the two linear equations to find the values of x and y.

Subtract equation (1) from equation (2), and we get,

2x=6

[tex]x=\frac{6}{2}\\[/tex]

x=3

Substitute the value of x in equation (1), and we get,

4(3)+2y=20

12+2y=20

2y=20-12

2y=8

[tex]y=\frac{8}{2}\\[/tex]

y=4

Number of cows=3

Number of ducks=4

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Answer:

  (a)  x = 12

Step-by-step explanation:

The radicals in this equation can be eliminated simply by squaring both sides. Then the resulting linear equation is solved in two steps.

__

  [tex]\left(\sqrt{2x-8}\right)^2=\left(\sqrt{x+4}\right)^2\\\\2x-8=x+4\qquad\text{simplify}\\\\x-8=4\qquad\text{subtract $x$}\\\\\boxed{x=12}\qquad\text{add 8}[/tex]

_____

Additional comment

You know the contents of each radical must not be negative. That means 2x-8 ≥ 0, or x≥4. We know x=4 doesn't work in the equation (0≠√8), so we only need to check the answers x=12 and x=7. Of those, only x=12 satisfies the equation.

Answer:

y = - 3x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 2) and (x₂, y₂ ) = (0, - 1)

m = [tex]\frac{-1-2}{0-(-1)}[/tex] = [tex]\frac{-3}{0+1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3

the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = - 3x - 1 ← equation of line

Answer:

Common difference:  30

General term formula:   [tex]a_n=30n-9[/tex]

52nd term:  1551

Step-by-step explanation:

Given sequence:

21, 51, 81, 111

Calculate the difference in terms:

[tex]21 \underset{+30}{\longrightarrow} 51 \underset{+30}{\longrightarrow} 81 \underset{+30}{\longrightarrow} 111[/tex]

The sequence is increasing by 30 each time, so as there is a common difference, this is an arithmetic sequence with a common difference of 30.

General form of an arithmetic sequence

[tex]a_n=a+(n-1)d[/tex]

where:

Given:

Substitute the given values into the formula to find the general term formula:

[tex]\implies a_n=21+(n-1)30[/tex]

[tex]\implies a_n=21+30n-30[/tex]

[tex]\implies a_n=30n-9[/tex]

To find the 52nd term, simply substitute n = 52 into the found general term formula:

[tex]\implies a_{52}=30(52)-9[/tex]

[tex]\implies a_{52}=1560-9[/tex]

[tex]\implies a_{52}=1551[/tex]

Answer:

D

Step-by-step explanation:

Trust me

Answer:

f < 0

Step-by-step explanation:

33 + 6f < 33 ( subtract 33 from both sides )

6f < 0 ( divide both sides by 6 )

f < [tex]\frac{0}{6}[/tex] , that is

f < 0

[tex]\\ \rm\Rrightarrow log_5512[/tex]

[tex]\\ \rm\Rrightarrow log_52^9[/tex]

[tex]\\ \rm\Rrightarrow 9log_52[/tex]

[tex]\\ \rm\Rrightarrow 9\dfrac{log2}{log5}[/tex]

[tex]\\ \rm\Rrightarrow 3.876[/tex]

If your question is something different let me know by which I can change my answer

Answer:

3.876  (3 d.p.)

Step-by-step explanation:

Given:

Please note:  The question gives two values of log base 10 which should be used to help find the value of [tex]\log_5512[/tex]

Log Law:  Change of Base

[tex]\log_ba=\dfrac{\log_xa}{\log_xb}[/tex]

Change the given expression to log base 10:

[tex]\implies \log_5512=\dfrac{\log_{10}512}{\log_{10}5}[/tex]

Replace 512 with 2⁹, and 5 with 10/2:

[tex]\implies \dfrac{\log_{10}{2^9}}{\log_{10}\frac{10}{2}}[/tex]

[tex]\textsf{Apply the Power Log law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies \dfrac{9\log_{10}{2}}{\log_{10}\frac{10}{2}}[/tex]

[tex]\textsf{Apply the Log Quotient law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay[/tex]

[tex]\implies \dfrac{9\log_{10}{2}}{\log_{10}10-\log_{10}2}[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies \dfrac{9\log_{10}{2}}{1-\log_{10}2}[/tex]

Given:

Substitute this into the expression and simplify:

[tex]\implies \dfrac{9(0.3010)}{1-0.3010}[/tex]

[tex]\implies \dfrac{2.709}{0.699}[/tex]

[tex]\implies 3.876\:(\sf 3\: d.p.)[/tex]

The area of the water well is [tex]4\pi r^2[/tex]

The radius is given as:

Radius, R = 2r

The area of the water well is calculated using:

[tex]A = \pi R^2[/tex]

This gives

[tex]A = \pi (2r)^2\\\\\\[/tex]

Evaluate the expression

[tex]A = 4\pi r^2[/tex]

Hence, the area of the water well is [tex]4\pi r^2[/tex]

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )= \dfrac{3}{2} \sqrt{x} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)= \cfrac{- 3}{ {x}^{4} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)= \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

properties to be used here :

[tex]\qquad \tt \rightarrow \:\cfrac{d}{dx}( {x}^{ n } ) = n \sdot{x}^{n - 1} [/tex]

[tex]\large \textsf{Question : 1} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )[/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3}{2} - 1 } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3 - 2}{2} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{1}{2} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} \sqrt{x} [/tex]

[tex]\large \textsf{Question : 2} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - 3} } )[/tex]

[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 3 - 1} } [/tex]

[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 4} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{- 3}{ {x}^{4} } [/tex]

[tex]\large \textsf{Question : 3} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{{x}^{ \frac{1}{2} } } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - \frac{1}{2} } } )[/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ - \frac{1}{2} - 1} } [/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 1 - 2}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 3}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2{x}^{ \frac{ 3}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

2

Step-by-step explanation:

because it's for the point s

The radical equation from the following equation is 3+x√7=13, the correct option is C.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that;

Four equations

x+√5=12, x² = 16, 3+x√7=13, 7√x = 14

Now,

Out of the four options you gave, only one is a radical equation:

Ox+√5=12 O x² = 16 O 3+x√7=13 O 7√x = 14

Only 3+x√7=13 because x is under a cube root sign. The other options are not radical equations because they do not have variables under radicals.

Therefore, the radical equation will be 3+x√7=13.

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it is a bracket used in maths

Answer:

They are kind of like outer brackets, so if you have some expression like this:

5 + (4 × 6 + (7 - 8)),

it's better to write it like this:

5 + [4 × 6 + (7 - 8)],

so you can read it more easily.

Answer: 48

Step-by-step explanation:

We need to find the least common multiple of 12 and 16.

Finding the prime factorizations of 12 and 16,

[tex]12=2^{2} \times 3\\\\16=2^{4}[/tex]

Thus, the least common multiple is [tex]2^{4} \times 3=\boxed{48}[/tex]

Answer:

i don't know

Step-by-step explanation:

i don' know

5[tex]\sqrt{3}[/tex]

Special right triangles, such as the one shown, have unique equations that can be used to find missing sides.

30-60-90 Triangles

The angle measurements show us that this is a 30-60-90 triangle. This name refers to the 3 angle measurement. There are 2 types of special right triangles, 45-45-90 and 30-60-90. For most triangles, it would take the law of sine or cosine to find a missing side with only 1 side given. But, with special right triangles, we can use shortcuts to find a.

Formulas

For all 30-60-90 triangles, there are 3 sides: the hypotenuse (c), the long leg (a), and the short leg (b). The shortcuts for 30-60-90 triangles are based on the length of the short leg.

The formulas are as follows (the variables match the variable given in the figure):

Solving for a

So, to find a, we must first find b. Since b is equal to half of c, we can divide the value of c by 2.

Thus, b = 5

Next, plug this value into the formula for b

Answer:

Last option

Step-by-step explanation:

cos30° = a/10  

a = 10cos30°

     [tex]cos30=0.8660=\frac{\sqrt{3} }{2}[/tex]

[tex]a=10(\frac{\sqrt{3} }{2} )=5\sqrt{3}[/tex]

Hope this helps

It has a period of 2pi

the equation to find the period of a sin/cos function is

[tex]period = \frac{2\pi}{b} [/tex]

y = -2 sin(x) has a normal period of 2pi because the b value in this equation isn't stated, making it equal to 1

the basic equation for a sin function is

[tex]y = a \: \sin(b(x - c) ) + d[/tex]

The correct option is second one i.e 7x = 3

Therefore the results from adding the equation in this system are

7x = 3

Equations as,

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

  2x+y=8   .......................1

    5x-y=-5   .......................2

Result when adding equations 1 and 2 =?

On adding equations 1 and 2 the y term will get canceled and the like terms will combine is add (2x and 5x ) and ( 8 and - 5) as shown below

         2x    +    y    = 8

         5x   -   y     = - 5

-------------------------------------------

         7x     + 0        =   3

---------------------------------------------

Therefore the results from adding the equation in this system are 7x=3.

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Answer:

7x=3

Step-by-step explanation:

Answer:

hes a titan

Step-by-step explanation:

Answer: 137.5 in

Step-by-step explanation: All we have to do is multiply 25 to 5.5 to get the original result. Since the scaling is 1/25, it means it is 25 times smaller. Thus, just multiply 25 to 5.5 and you get 137.5 in, the original result.

Answer:

Step-by-step explanation:

Comment

x and 133 sit on the the same straight line with MO in common. Therefore they are supplementary which means that the add to 180o.

Equation

x + 133 = 180

Solution

Subtract 133 from both sides

x + 133 = 180                    

x + 133 - 133 = 180 - 133

x = 47 degrees.

Answer

x = 47

The equation of the line will be y = 4x. Then the correct option is A.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

Writing an Equation from a Table

A 2-column table with 6 rows. Column 1 is labeled x with entries 8, 12, 16, 20, 24, 28. Column 2 is labeled y with entries 2, 3, 4, 5, 6, 7.

Then at (2, 8) and (3, 12), we have

y – 8 = [(12 – 8) / (3 – 2)] (x – 2)

y – 8 = 4x – 8

     y = 4x

Then the correct option is A.

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The synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) =  2x³ + 2x + 4.

The division of the polynomial is determined as follows;

(2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2)

                     2x³ + 2x + 4

                   -------------------------

     x + 2   √(2x⁴ + 4x³ + 2x² + 8x + 8)

                - (2x⁴ + 4x³)

                 -------------------------------------

                                        2x² + 8x + 8

                                     - (2x² + 4x)

                                   ------------------------

                                                  4x + 8

                                               - (4x + 8)

                                              -------------------

                                                       0

Thus, the synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) =  2x³ + 2x + 4.

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A comparison of the actual number of people who violate the speed limit to the total number of drivers is an example of a rate

A rate is known as the quantity measured with respect to another measured quantity. It refers to the comparison of a part to a whole.

It is also the measure of a part with respect to a whole or a proportion.

Therefore, a comparison of the actual number of people who violate the speed limit to the total number of drivers is an example of a rate

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Answer:

dummy its 23 bc angel A

Step-by-step explanation:

WRITE iT dOwN nOW dUmMy

Answer:

x = 2, y = 1 or (2, 1)

Step-by-step explanation:

Solving by elimination method :

The solution is : x = 2, y = 1 or (2, 1)

Answer:

Dimensions = 8 CM and 12 CM

length = 12 CM

width = 8 cm

perimeter = 2 ( length + width)

= 2( 12 + 8)

= 2 ( 20)

= 40 CM

ratio = 12/40

= 6/20

= 3/10

Answer:

8

Step-by-step explanation:

let the ratio constant be 'x'

=> 2x:3x

sum = 2x + 3x = 5x

Total number of boys

=>(2x/5x)20 = 8

The ratio of boys and girls in a classroom is 2 : 3 respectively. If the total number of children is 20. How many boys are there in the class ?

In this question we are provided with the ratio of boys isto girls that is 2 : 3 it is also given that total number of children are 20. We are asked to calculate number of boys.

[tex] \green{ \small \pmb{\tt{ First \: we \: will \: form \: an \: equation }}}[/tex]

Let us assume the number of girls as 3x and number of boys as 2x.

Total number of children = 20

3x + 2x = 20

[tex] \orange{\small \pmb{\tt{ Now \: we \: will \: solve \: this \: equation }}}[/tex]

[tex] \small\frak{ 3x + 2x = 20}[/tex]

[tex] \small\frak{ 5x = 20}[/tex]

[tex] \small\frak{ x = \dfrac{20}{5} = 4}[/tex]

[tex] \small \underline{ \boxed{\pmb{x = 4} }} \large \: \star[/tex]

Boys = 2 × 4 = 8

Girls = 3 × 4 = 12

[tex] \tiny \tt{spbankingandsscseries}[/tex]

Answer:

8/15

Step-by-step explanation:

For right triangles tan p = opposite leg / adjacent leg

tan p = 24 /45   =   8/15