Simplify surd need an answer asap please

Simplify Surd Need An Answer Asap Please

Answers

Answer 1

Answer:

Step-by-step explanation:

Simplify Surd: Multiply the denominator and numerator with the conjugate of the denominator.Conjugate of denominator:

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

[tex]\sf\dfrac{\sqrt{x+1} +\sqrt{x-1}}{\sqrt{x+1}-\sqrt{x-1}} = \dfrac{(\sqrt{x+1} +\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}{(\sqrt{x+1} -\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}\\[/tex]

           When doing so, in the numerator, we get in the form of the identity (a +b)² and in the denominator a² - b²

                            [tex]\sf =\dfrac{(\sqrt{x+1} +\sqrt{x-1})^2}{(\sqrt{x+1})^2 - (\sqrt{x-1})^2}\\\\=\dfrac{(\sqrt{x+1})^2+(\sqrt{x-1})^2+2*\sqrt{x+1}*\sqrt{x-1}}{x + 1 - (x - 1)}\\\\=\dfrac{x+1 +x -1 + 2*\sqrt{(x+1)(x-1)}}{x + 1 - x + 1}\\\\=\dfrac{x+ x + 1 - 1 +2\sqrt{x^2-y^2}}{x-x+1+1}\\\\=\dfrac{2x+2\sqrt{x^2-y^2}}{2}\\\\= \dfrac{2x}{2}+\dfrac{2\sqrt{x^2-y^2}}{2}\\\\=x + \sqrt{x^2-y^2}[/tex]


Related Questions

the distance on a ruler between 8cm and 26cm =

Answers

Answer:

18 cm

Step-by-step explanation:

To find the distance, take the larger number and subtract the smaller number

26 cm - 8 cm

18 cm

4.
Solve the system of inequalities graphically. Label the solution set with an S.
Help asap

Answers

Answer:

Solution = (2,1)

Step-by-step explanation:

Make them equal each other and solve for x.

2x - 3 = 1

2x = 4

x = 2

2 * 2 - 3 = 1

Solution = (2,1)

Suppose y varies inversely with x, and y = 49 when x = 17. What is the value of x when y = 7 ?

Answers

[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\underline{y} varies inversely with \underline{x}}}{y=\cfrac{k}{x}}\qquad \textit{we also know that} \begin{cases} y=49\\ x=17 \end{cases} \\\\\\ 49=\cfrac{k}{17}\implies 833=k~\hfill \boxed{y=\cfrac{833}{x}} \\\\\\ \textit{when y = 7, what is "x"?}\qquad 7=\cfrac{833}{x}\implies x=\cfrac{833}{7}\implies x=119[/tex]

F. In what order should items weighing
51 pounds, 40 pounds, 48 pounds,
and 44 pounds be stacked if you want
them in order from heaviest to lightest?

Answers

Answer:

51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.

Which points are solutions to the system of inequalities shown below? Check all that apply.
y > x
y > 2
x > 4
A.(6, 4)
B.(9, -2)
C.(4, 2)
D.(9, 10)
E.(8, 1)
F.(5, 6)

Answers

Answer: D and F

Step-by-step explanation:

For the first inequality, we know that y>x, so this eliminates options A, B, C, and E. This means we only need to check D and F.

Both D and F have a y coordinate greater than 2 and an x coordinate greater than 4, so they are both correct.

The diameter of a circle is 94 cm.
By first calculating the radius, work
out the area of the circle.
2
Give your answer in cm² to 1 d.p.

Answers

Given:d= 94 cmNote that:d= Diameter To find:The radius of the circle The area of the circleSolution:

[tex]\huge\boxed{Formula: r= \frac{d}{2}}[/tex]

Substitute the values according to the formula.

[tex]r=\frac{94}{2}[/tex]

[tex]\large\boxed{r=47 \: cm}[/tex]

Now, let's find the area.

[tex]\huge\boxed{Formula:a= \pi{r}^{2}}[/tex]

So, we'll have to multiply π, 47 and 47.

Substitute the values according to the formula.

[tex]a= \pi{47}^{2}[/tex]

[tex]a= 6939.778172 \: {cm}^{2}[/tex]

[tex]\large\boxed{a= 6939.8 \: {cm}^{2}(1 \: d.p)}[/tex]

Hence, the area of the given circle is 6939.8 square centimeters.

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the radius & area of the circle.

To find the [tex]\star\bf{radius}\star[/tex], we divide the diameter by 2:

[tex]\star~\bf{94\div2}[/tex]

[tex]\star~\bf{Radius=47}\star[/tex]

Now that we have the radius, let's compute the area! :)

///\\\///\\\///\\\///\\\///\\\////\\\///\\///\\\///\\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\//\\\//\\

                            Calculating the Area

We can work out the area of a circle by using this formula:

[tex]\star\boxed{\pmb{A_{(circle)}=\pi r^2}}\star[/tex]

Where

[tex]\dag[/tex] A=Area of a circle

[tex]\dag[/tex] [tex]\pi =3.14...[/tex]

[tex]\dag[/tex] r=radius

Have you noticed the [tex]\large\pmb{^2}[/tex] next to r? This tells us that we should multiply the radius times itself.

Now it's time to substitute the values:

[tex]\star~\large\pmb{A=3.14\times47^{2}}\star[/tex]

Let's simplify it. The acronym PEMDAS will help us, and we won't make any mistakes in the Order of Operations! :)

Here's what it stands for:

P=Parentheses

E=Exponents

M=Multiplication

D=Division

A=Addition

S=Subtraction

2 is an exponent.

So what do you think we should do first?

[tex]\square[/tex] Square 47.

[tex]\square[/tex] Multiply 3.14 times 47 and then square.

That's right, we should square 47 first. :)

[tex]\star~\large\pmb{A=\pi \times2209}}\star[/tex]

Now, according to PEMDAS, we should multiply pi times 2209; after multiplying, we obtain:

[tex]\star~\large\pmb{A=6936.8\:cm^2}\star[/tex]

Remember, the area of any shape is measured in units squared.

[tex]\ddot\bigstar[/tex] Remember this...

[tex]\fbox{\bf{The\;area\;of\;any\;shape\;is\;measured\;in\;units\;squared}}[/tex]

Hope this helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

[tex]\bigstar\footnotesize\pmb{M^ar_ib^el\;Peri}[/tex]

In triangle ABC, AP is an angle bisector of angle BAC. What is the length of PC? Round you answer to the nearest whole number.
A) 6 B) 7 C) 8 D) 9

Answers

Answer:

D) 9

Step-by-step explanation:

x = ½ × 13 = 6.5

y = ½ × 5 = 2.5

6.5 + 2.5 = 9

So the length of PC is 9

HOPE THIS HELPS AND HAVE A NICE DAY <3

Right triangle ABC is reflected over AC, then dilated by a scale factor of Two-thirds to form triangle DEC. Which statements about the two triangles must be true? Select three options.

△ABC ~ △DEC
∠B ≅ ∠E
3BC = 2EC
3DE = 2AB
3m∠A = 2m∠D
2m∠A = 3m∠D

Answers

The triangle △ABC and △DEC are similar to each other. Then the correct option is A, B, and D.

What is a transformation of a point?

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

Right triangle ABC is reflected over AC.

Then dilated by a scale factor of Two-thirds to form triangle DEC.

The triangle △ABC and △DEC are similar to each other.

△ABC ≅ △DEC

The dilation is 2/3. Then we have

DE / AB = 2 / 3

     3AB = 2DE

∠B ≅ ∠E = 90

There is no effect of dilation on angle.

Then the correct option is A, B, and D.

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Answer:

A. △ABC ~ △DEC

B. ∠B ≅ ∠E

D. 3DE = 2AB

Step-by-step explanation:

got it right on edge 23

The table shown below lists the time, in days, that it takes for
a package to be delivered based on its mode of transport and
whether it is international or domestic. Some additional
information is provided.
1. The cost per package by air is $100; by train, $50; by
truck, $10; and by boat, $20.
2. Fragile packages cannot be transported by air.
3. Shipping fragile packages costs an extra $20.
4. Shipping international packages costs an extra $30.
Tim needs to transport a fragile package, and he needs it to
arrive as soon as possible. He is shipping domestic. Which of
the following shipping methods should he use?

Answers

Answer:gotchu g there it is

Step-by-step explanation:

Answer:sike gtf

Step-by-step explanation:

What is true of the function g(x) = -2x² + 5?
O g(x) is the multiplication of g and x.
O-212 +5 is the input of the function.
The variable x represents the independent variable.
The variable g represents the input of the function.

Answers

Answer:

C.) The variable x represents the independent variable

Step-by-step explanation:

The variable "x" is the independent variable because that is the value that we can manipulate. We cannot manipulate the dependent variable because it is determined by the independent variable. In that case, "y" would be the dependent variable because its value is dependent on what "x" is.

A.) is incorrect because g(x) symbolizes the input of the variable "x" into the g function.

B.) is incorrect because "x" is the input.

D.) is incorrect because "x" is the input.

what is the area of the figure?​

Answers

Answer:

area = 62ft

Step-by-step explanation

so you section the polygon into a big rectangle and 2 small rectangles

the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft

the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft

now add the areas you got, 50+12 which is 62ft

hope this helps:)

WILL MARK BRAINLIEST 50 POINTS Find the area of the regular pentagon if the apothem is 7 ft and a side is 10 ft. Round to the nearest whole number.



175 ft2

350 ft2

35 ft2

70 ft2

Answers

Answer:

175 ft^2

Step-by-step explanation:

split the pentagon into 5 triangles with base length 10ft and height 7ft. each triangle then has an area of 10 * 7 * 1/2 = 35 ft^2

then the pentagon has an area 35*5 = 175 ft^2

im lost can someone help?​

Answers

Type that into cymath, it’s free and it’s gives you all the work for free.

what is the median of the data set represented by the box plot shown below? 38,45,50,60,75

Answers

Answer:

50

Step-by-step explanation:

I need help solving this problem system of equations

Answers

Answer:

y= -6

Step-by-step explanation:

-4x and 4x are canceled out. -2y+8y= 6y. -12-24=-36

You are left with 6y=-36 . Divide from both sides and -36/6 is -6. So, y=-6.

Hope this helped.

Determine u-x and o-x from the given parameters of the population and the sample.size. round the answer to the nearest thousandth where appropriate u=27 o=5 n=14

Answers

The u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 5.

How to calculate the values?

From the information given about the population and sample mean, the values include:

u=27 o=5 n=14

The standard deviation will be:

= 5/✓14

= 5/3.74

= 1.34

Therefore, u-x and o-x from the given parameters of the population and the sample size will be u =28 and standard deviation is 1.34.

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A wooden roller is 1 m long and 8 cm in diameter. Find it's mass in grams if 1cm³ of the wood has a mass of 0.7 g​

Answers

Answer:

1120π grams

==> 3518.58 grams  using value of π = 3.14159 or

==> 3520 grams using value of π = 22/7

Step-by-step explanation:

Volume of a cylinder = πr²l where r is the radius of the base and h is the length of cylinder

The diameter of the cylinder, d = 8cm and radius = d/2 = 4cm

Length = 1 meter = 100 cm

Here, volume V = π.4².100 =  π x 16 x 100 = 1600π cm³

Since 1 cm³ has a mass of 0.7gm total mass
M = 0.7V = (0.7)1600π =1120π gm


Using the ratio 22/7 for pi we get
M =  1120 x 22/7  = 3520 g

If we use the more accurate value of π as 3.14159 then we get
M = 1120 x 3.14.159 = 3518.58 g which is more accurate

Find the slope and the y-intercept of the following linear equation. 5. 3x + 2y = 14​

Answers

The slope and y-intercept of the equation are - 3 / 2 and 7 respectively.

How to find slope and y-intercept?

The slope and y-intercept of an equation can be easily found using slope intercept equation.

y = mx + b

where

m = slopeb = y-intercept

Therefore,

3x + 2y = 14

2y = -3x + 14

y = -3 / 2 x + 7

Therefore,

slope = - 3 / 2

y-intercept = 7

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Draw and set up the integrals for the area enclosed by the y–axis, the curve y = (x + 1)1/2 and y = 2. Compute one of them.

Region II only please

Answers

If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set

[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]

and as a type II region,

[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]

where we solve y = √(x + 1) for x to get x as a function of y.

A. The area of the type I region is

[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]

B. The area of the type II region is of course also

[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]

I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).

can someone help me with this worksheet please!!!!

Answers

(1) The missing term in the sequence, a₁₂  = 0.8.

(2) The missing term in the sequence, a₈ = 102.5.

(3) The missing term in the sequence, a₈ = 111.

(4) The missing term in the sequence, a₁₂ = -19.

(5) The missing term in the sequence, a₁₂ = 94.

(6)  The missing term in the sequence, a₆ = 40.

(7)  The missing term in the sequence, a₃₆ = -52.

(8)  The missing term in the sequence, a₂₁ = -58.

Missing term of the sequence

The missing term in the sequence is determined as follows;

Tₙ = a + (n - 1)d

1.0 a₄ = 18.4 and a₅ = 16.2, a₁₂ = ?

T₄ = a + 3d

18.4 = a + 3d  ---(1)

T₅ = a + 4d

16.2 = a + 4d  ---(2)

subtract (1) from (2)

-2.2 = d

18.4 = a + 3(-2.2)

a = 25

a₁₂  = a + 11d

a₁₂  = 25 + 11(-2.2)

a₁₂  = 0.8

2.0 a₂ = 57.5 and a₅ = 80, a₈ = ?

a₂ = a + d

57.5 = a + d -- (1)

a₅ = a + 4d

80 = a + 4d  --- (2)

solve (1) and (2)

d = 7.5

a = 50

a₈ =  a + 7d

a₈ = 50 + 7(7.5)

a₈ = 102.5

3.0 a₁₀ = 141 and a₁₃ = 186, a₈ = ?

a₁₀ = a + 9d

141 = a + 9d --- (1)

a₁₃ = a + 12d

186 = a + 12d --- (2)

Subtract (1) from (2)

d = 15

a = 6

a₈ = a + 7d

a₈ = 6 + 7(15)

a₈ = 111

4.0 a₂₂ = -49 and a₂₅ = -58, a₁₂ = ?

a₂₂ = a + 21d

-49 = a + 21d ---- (1)

a₂₅ = a + 24d

-58 = a + 24d --- (2)

subtract (1) from (2)

d = -3

a = 14

a₁₂ = a + 11d

a₁₂ = 14 + 11(-3)

a₁₂ = -19

5.0 a₄ = -2 and a₈ = 46, a₁₂ = ?

a₄ = a + 3d

-2 = a + 3d --- (1)

a₈ = a + 7d

46 = a + 7d ---- (2)

Subtract (1) from (2)

d = 12

a = -38

a₁₂ = a + 11d

a₁₂ = -38 + 11(12)

a₁₂ = 94

6.0 a₉ = 64 and a₁₂ = 88, a₆ = ?

a₉ = a + 8d

64 = a + 8d --- (1)

a₁₂ = a + 11d

88 = a + 11d --- (2)

Subtract (1) from (2)

d = 8

a = 0

a₆ = a + 5d

a₆ = 0 + 5(8)

a₆ = 40

7.0 a₂₀ = -4 and a₂₃ = -13, a₃₆ = ?

a₂₀ = a + 19d

-4 = a + 19d ---- (1)

a₂₃ = a + 22d

-13 = a + 22d --- (2)

Subtract (1) from (2)

d = -3

a = 53

a₃₆ = a + 35d

a₃₆ = 53 + 35(-3)

a₃₆ = -52

8.0 a₂₈ = 5 and a₃₃ = 50, a₂₁ = ?

a₂₈ = a + 27d

5 = a + 27d ---- (1)

a₃₃ = a + 32d

50 = a + 32d --- (2)

Subtract (1) from (2)

d = 9

a = -238

a₂₁ = a + 20d

a₂₁ = -238 + 20(9)

a₂₁ = -58

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answer question below.

Answers

The speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.

What is speed?

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

Let the speed of the Elvira be x. Then the speed of the Altheia will be (x - 6).

Let the distance between the coffee shop and Elvira's house be d.

Then the distance between the coffee shop and Altheia's house will be (3.6 - d).

Then we have

x = d / 0.5 ...1

(x - 6) = (3.6 - d) / 0.6 ...2

In solving the equations 1 and 2, we have

x = 6.545 and d = 3.2725 miles

Then the speed of the Elvira is 6.545 miles per hour. Then the speed of the Altheia will be 0.545 miles per hour.

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If we changed the 3 to a 0 in the equation, what would happen to the graph?

Answers

A function assigns the values. The function will move down by 3 units.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

The graph of the function is given below. Now if 3 is replaced by a 0, then the y-intercept of the function will become zero while keeping the slope the same. Therefore, the function will move down by 3 units.

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If the given figure is sliced through points J. K. and L, which best describes the shape of the resulting cross-section?
A
OA parallelogram
OB. trapezoid
OC. rectangle
OD. triangle

Answers

The shape of the resulting cross-section will be equal to the trapezoid.

What is a trapezoid?

A trapezoid is a quadrilateral having four sides whose two sides are parallel to each other and the other two sides are nonparallel to each other.

As it is given in the question the figure is sliced through points J. K. and When the shape is sliced from the given points it will create the trapezoidal shape that will have two parallel sides and the other two sides are Non-parallel

Therefore the shape of the resulting cross-section will be equal to the trapezoid.

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Answer:

Trapezoid

Step-by-step explanation:

I got it right on Edmentum

Hook me up with a 5 star and a thanks :)

Determine whether each triangle with sides of given length is a right triangle. justify your answer
7 yd, 5 yd, 9 yd
10 ft, 24ft, 26 ft

Answers

The triangles with the side lengths 10 ft, 24ft, 26 ft, is a right triangle while a triangle with side lengths of 7 yd, 5 yd, 9 yd is NOT based on the Pythagorean theorem.

What is a Right Triangle?

A triangle is said to be a triangle based on the Pythagorean theorem, if the square of the longest side equals the sum of the squares of the other smaller sides of the triangle.

9² = 7² + 5²

81 = 74 (NOT TRUE), therefore, the triangle with the side lengths 7 yd, 5 yd, 9 yd, is not a right triangle.

26² = 10² + 24²

676 = 676 (TRUE), therefore, the triangle with the side lengths 10 ft, 24ft, 26 ft, is a right triangle.

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Review the graph of complex number z.

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z is at (negative 3, 1).

What is the modulus of z?

2
2StartRoot 2 EndRoot
3
StartRoot 10 EndRoot

Answers

Answer:

√10

Step-by-step explanation:

[tex]\text {modulus of z } = =\sqrt{\left( -3\right)^{2} +\left( 1\right)^{2} } =\sqrt{9+1} =\sqrt{10}[/tex]

Answer:

square root of 10

Step-by-step explanation:

The square below represents one whole.
Express the shaded area as a fraction, a decimal, and a percent of the whole.

Answers

The shaded area expressed as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively

Fractions, Decimals and Percentages

From the question, we are to express the shaded area as a fraction, a decimal, and a percent of the whole.

In the diagram, there are 100 total squares and 23 of them are shaded

Expressing the shaded area as a fraction, we get

[tex]\frac{23}{100}[/tex]

Expressing the shaded area as a decimal, we get

[tex]\frac{23}{100}[/tex] = 0.23

Expressing the shaded area as a percent , we get

[tex]\frac{23}{100}\times 100\%[/tex] = 23%

Hence, the shaded area as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively

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Please solve these questions!! preferrably today since the quarter locks today!!

Answers

Answer:

131

Step-by-step explanation:

Write two numbers that multiply to the value on top and add to the value on bottom.
-84
17

Answers

Two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.

What is multiplication?

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. Multiplication essentially means the repeated addition.

The two given numbers are -84 and 17.

We need to write two numbers that multiply to the value on top (-84) and add to the value on the bottom (17).

If we multiply 21 and -4, we get the product as -84.

That is, 21×(-4)=-84

If we add 21 and -4, we get the sum as -17.

That is, 21+(-4)=21-4=17

Therefore, two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.

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PLEASE HELP!!!!!!!!!!!!!!!!!!! I'll NAME BRAINLIEST!!!!!!!!!!!!!!!!!A moving-van rental company uses the polynomial 110 + 0.65(m – 200) to calculate the rental charges if a customer drives a van more than 200 miles in one day. In the polynomial, m is the total number of miles that the customer drove the van during the day. Use the Distributive Property to write an equivalent expression for the total cost of renting the van and driving it more than 200 miles in one day.

Answers

Answer:I think it would be 84 + 0.45m + 108.

Which simplified could be 0.45m + 192.

hope this helps!

Step-by-step explanation:

Given that 24w = 14ten .Find the unknown base​

Answers

Answer:

w = 5

Step-by-step explanation:

24w = (14)10

2w + 4 = 10 + 4

2w = 10

w = 5

Other Questions
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