4 times a number divided by 3 is 5 more than that number divided by 2 what is the value of that number

Answers

Answer 1

Answer:

x=6

Step-by-step explanation:

Let the number be x

Then 4 times a number divided by 3 is 5 more than that number divided by 2 gives the equation:

[tex] \frac{4x}{3} = \frac{x}{2} + 5[/tex]

Multiply through by the LCD, which is 6.

[tex] 6 \times \frac{4x}{3} = 6 \times \frac{x}{2} + 5 \times 6[/tex]

Cancel out to obtain:

[tex] 2 \times 4x =3 \times x + 30[/tex]

[tex]8x = 3x + 30[/tex]

Group similar terms

[tex]8x - 3x = 30[/tex]

Simplify the LHS

[tex]5x = 30[/tex]

Divide both sides by 5 to get:

[tex]x = 6[/tex]


Related Questions

Find the area for the following figure.
A. 51.06m^2
B. 74.98 m^2
C. 27.14m^2
D. 102.1^2

Answers

area = sum of parallel sides . height/2

= (5.9 + 16.3) 4.6/2

= 22.2 . 2.3

= 51.06 m²

so the answer is A

When an article was sold for #14
the profit was 40% What would
have been the proft, if it had
been sold for #16?​

Answers

Answer:

45.7%

Step-by-step explanation:

16/14*40%=45.7%

The correct statement is that the profit is 60% if it had been sold for $16.

What is the percentage?

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.Triangle?

Given

When an article was sold for $14 the profit was 40%.

How to find the profit if it had been sold for $16?​

When an article was sold for $14 the profit was 40%.

Then, the cost of the article will be $10.

If the article is sold for $16.

Then profit will be

[tex]\rm Profit = \dfrac{selling\ price \ - \ cost\ price}{cost\ price}*100\\\\\rm Profit = \dfrac{16-10}{10}*100\\\\\rm Profit = 60 \%[/tex]

Thus, the profit will be 60%.

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rationalize √3+√2/√3-√2​

Answers

Answer:

5 + 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Multiply top and bottom by sqrt(3) + sqrt(2)

Top = (sqrt (3) + sqrt(2)) * (sqrt(3) + sqrt(2))

Top = 3 + sqrt(6) + sqrt(6) + 2

Top = 5 + 2sqrt(6)

Bottom = (sqrt (3) - sqrt(2)) * (sqrt(3) + sqrt(2))

Bottom = (3 - sqrt(6) + sqrt(6) - 2)

Bottom = 1

So, the answer is 5 + 2[tex]\sqrt{6\\}[/tex]

Answer: 5+2√6

Step-by-step explanation: attachment

Find all real solutions of the quadratic equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)
x2 − 6x + 1 = 0

Answers

Answer:

x= 1÷4

Step-by-step explanation:

2x - 6x + 1 =0

-4x + 1= 0

-4x = -1

Final answer:

Using the quadratic formula, the real solutions of the equation [tex]x^2 - 6x + 1 = 0[/tex]are x = 3 + 2√2 and x = 3 − 2√2 since the discriminant is positive, indicating two real solutions.

Explanation:

To find all real solutions of the quadratic equation  [tex]x^2 - 6x + 1 = 0[/tex], we can use the quadratic formula, which is x = −b ± √(b2 − 4ac) / (2a) where a, b, and c are coefficients from the equation in the form [tex]ax^2 + bx + c = 0[/tex]. For our equation, a = 1, b = −6, and c = 1. Let's apply these values into the formula:

Calculate the discriminant: (−6)2 − 4(1)(1) = 36 − 4 = 32.

Since the discriminant is positive, there are two real solutions.

Calculate the solutions: x = (6 ± √32) / (2 × 1) = (6 ± 4√2) / 2 = 3 ± 2√2.

The real solutions of the equation are x = 3 + 2√2 and x = 3 − 2√2.

-3(-4n + 30) = -30 Answer please?​

Answers

Answer:

n = 5

Step-by-step explanation:

Step  1  :

Step  2  :

Pulling out like terms :

2.1     Pull out like factors :

  -4n + 30  =   -2 • (2n - 15)

Equation at the end of step  2  :

 (0 -  -6 • (2n - 15)) -  -30  = 0

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  12n - 60  =   12 • (n - 5)

Equation at the end of step  4  :

 12 • (n - 5)  = 0

Step  5  :

Equations which are never true :

5.1      Solve :    12   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

5.2      Solve  :    n-5 = 0

Add  5  to both sides of the equation :

                     n = 5

One solution was found :

                  n = 5

Processing ends successfully

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To solve this, you need to isolate/get the variable "n" by itself in the equation:

-3(-4n + 30) = -30        Divide -3 on both sides

[tex]\frac{-3(-4n+30)}{-3} =\frac{-30}{-3}[/tex]     [two negative signs cancel each other out and become positive]

-4n + 30 = 10       Subtract 30 on both sides

-4n + 30 - 30 = 10 - 30

-4n = -20          Divide -4 on both sides to get "n" by itself

[tex]\frac{-4n}{-4}=\frac{-20}{-4}[/tex]

n = 5

PROOF

-3(-4n + 30) = -30       Substitute/plug in 5 into "n"

-3(-4(5) + 30) = -30

-3(-20 + 30) = -30      Simplify what's inside the parentheses  [PEMDAS}

-3(10) = -30

-30 = -30

A box measure 4 inches long x 7 inches deep x 13 inches high. What's it's volume in cubic inches

Answers

Answer:

364 inches cubed

Step-by-step explanation:

Answer:

364 inches cubed

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well, the formula for volume is L*H*W

L=4 in, H=13 in, W=7 in

4*13*7=364

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

Emily rides her horse with a constant
speed of 12 km/h. How far can she travel
in 75 minutes?

Answers

Answer:

Step by-step explanation:

Speed v = 12km/h = 12/60km/min

Time t = 75min =

Distance d = ?

V = d/t

12/60 = d/75

Cross multiply

60d = 75 × 12

60d = 900

d = 900/60

d = 15km

Find the Quotient.
1,382 divided 4

Answers

Answer:

The quotient is 345.5

Step-by-step explanation:

Check image

Final answer:

To find the quotient of 1,382 divided by 4, divide each place value separately. The quotient is 343 with a remainder of 2.

Explanation:

To find the quotient of 1,382 divided by 4, we divide the thousands, hundreds, tens, and ones place separately. Starting from the leftmost digit, we divide 1,382 by 4.

4 divided by 1 is 0 with a remainder of 4. Bring down the next digit 3. So, we have 43. Next, divide 43 by 4. 4 divided by 43 is 10 with a remainder of 3. Bring down the next digit 8. So, we have 38. Finally, divide 38 by 4. 4 divided by 38 is 9 with a remainder of 2.

Therefore, the quotient of 1,382 divided by 4 is 343 remainder 2.

Lisa spots the mother bird on a branch above the nest. She
measures an angle of elevation to the bird of 67degrees. Find how
high the mother bird is above the ground, to the nearest foot.

Answers

To complete the calculations, more data is needed. We only have the angle of elevation of the mother bird, we need one relevant data, as for example, the distance from Lisa to the tree. We'll assume it to be 20 feet.

Answer:

The mother bird is 47 feet above the ground

Step-by-step explanation:

Right Triangles

They are a special type of triangles that have an internal angle of 90°. In such conditions, the following trigonometric relationship is valid:

[tex]\displaystyle tan\theta=\frac{y}{x}[/tex]

Where [tex]\theta[/tex] is the angle of elevation, y is the height of the triangle and x is the horizontal distance to the vertical leg

We can easily find the height of the tree by solving for y

[tex]y=xtan\theta[/tex]

[tex]y=20tan67^o[/tex]

[tex]y=47\ feet[/tex]

The mother bird is 47 feet above the ground

12 5/6x - 14x + 1/6x ?

Answers

The result of the given expression 12 5/6x - 14x + 1/6x  is -x

Given the expression

12 5/6x - 14x + 1/6x

Convert the mixed fractions into improper fractions as shown:

[tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]

Collect the like terms;

[tex]= \frac{77}{6} x+\frac{1}{6}x - 14x\\= \frac{77x+x}{6} - 14x\\= \frac{78x}{6} - 14x\\= 13x - 14x\\= -x[/tex]

Hence the result of the given expression is -x

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The simplified form of the expression is -x .

Given, expression [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex] .

Expression:  [tex]12\frac{5}{6}x -14x + \frac{1}{6} x[/tex]

Firstly solve the mixed fraction.

[tex]12\frac{5}{6} x\\= \frac{77}{6}x[/tex]

Rewriting the expression :

= [tex]\frac{77}{6}x - 14x + \frac{1}{6}x[/tex]

Solve the terms with common denominator.

= [tex]\frac{77+1}{6} x[/tex]

= [tex]13x[/tex]

Solve the like terms,

[tex]= 13x - 14x\\\\=- x[/tex]

Hence the simplified form of expression is -x .

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prove that, tan θ ( 1 + cot ^ 2 θ ) / ( 1 + tan ^ 2 θ ) = cot θ

Answers

Answer:

(identity has been verified)

Step-by-step explanation:

Verify the following identity:

tan(θ) (cot(θ)^2 + 1)/(tan(θ)^2 + 1) = cot(θ)

Multiply both sides by tan(θ)^2 + 1:

tan(θ) (cot(θ)^2 + 1) = ^?cot(θ) (tan(θ)^2 + 1)

(cot(θ)^2 + 1) tan(θ) = tan(θ) + cot(θ)^2 tan(θ):

tan(θ) + cot(θ)^2 tan(θ) = ^?cot(θ) (tan(θ)^2 + 1)

cot(θ) (tan(θ)^2 + 1) = cot(θ) + cot(θ) tan(θ)^2:

tan(θ) + cot(θ)^2 tan(θ) = ^?cot(θ) + cot(θ) tan(θ)^2

Write cotangent as cosine/sine and tangent as sine/cosine:

sin(θ)/cos(θ) + sin(θ)/cos(θ) (cos(θ)/sin(θ))^2 = ^?cos(θ)/sin(θ) + cos(θ)/sin(θ) (sin(θ)/cos(θ))^2

(sin(θ)/cos(θ)) + (cos(θ)/sin(θ))^2 (sin(θ)/cos(θ)) = cos(θ)/sin(θ) + sin(θ)/cos(θ):

cos(θ)/sin(θ) + sin(θ)/cos(θ) = ^?(cos(θ)/sin(θ)) + (cos(θ)/sin(θ)) (sin(θ)/cos(θ))^2

(cos(θ)/sin(θ)) + (cos(θ)/sin(θ)) (sin(θ)/cos(θ))^2 = cos(θ)/sin(θ) + sin(θ)/cos(θ):

cos(θ)/sin(θ) + sin(θ)/cos(θ) = ^?cos(θ)/sin(θ) + sin(θ)/cos(θ)

The left hand side and right hand side are identical:

Answer: (identity has been verified)

By using the Pythagorean trigonometric identities and substituting the expressions of tan θ, sec θ, and csc θ, we can simplify the given expression to prove that tan θ (1 + cot2 θ) / (1 + tan2 θ) equals cot θ.

To prove that tan θ ( 1 + cot2 θ ) / ( 1 + tan2 θ ) = cot θ, we can use trigonometric identities. Recall the Pythagorean identity which states that cot2 θ + 1 = csc2 θ and tan2 θ + 1 = sec2 θ. Using these identities, we can rewrite the expression on the left side of the equation:

tan θ ( 1 + cot2 θ ) / ( 1 + tan2 θ ) = tan θ * csc2 θ / sec2 θ

Since sec θ = 1/cos θ and csc θ = 1/sin θ, and remembering that tan θ = sin θ / cos θ, we substitute these into the expression:

tan θ * csc2 θ / sec2 θ = (sin θ / cos θ) * (1/sin2 θ) / (1/cos2 θ)

With simplification, the sin2 θ in the numerator and denominator cancel out, as do the cos2 θ terms, leaving us with:

cos θ / sin θ = cot θ

Thus, the original expression simplifies to cot θ.

Mr. and Mrs. Lorenzo want to buy a home valued at $213,500. If they have 18% of this amount saved for a down payment, how
much have they saved?
a $384.30
b. $3,843.00
C. $38,043.00
d. $38,430.00

Answers

Answer:D

Step-by-step explanation:

Multiply the cost of the house by 0.18.

Answer:DStep-by-step explanation:Multiply the cost of the house by 0.18.

What's greater 3/10,1/2,2/5?

Answers

[tex]\text{Hey there!}[/tex]

[tex]\bf{What\ is\ greater: \dfrac{3}{10}, \dfrac{1}{2},\&\dfrac{2}{5}?}[/tex]

[tex]\bf{Well, let's\ turn\ our\ fractions\ into\ decimals\downarrow}[/tex]

[tex]\bullet\ \bf{\dfrac{3}{10}=0.30(also\ known\ as\ 0.3)}\\\\\bullet \ \bf{\dfrac{1}{2}=0.50(also\ known\ as\ 0.5)}\\\\\bullet \ \bf{\dfrac{2}{5}=0.40(also\ known\ as\ 0.4)}[/tex]

[tex]\bf{The\ fractions\ in\ percentages\downarrow}[/tex]

[tex]\bullet \ \mathsf{\dfrac{3}{10}=30\%}\\\\\bullet \ \mathsf{\dfrac{1}{2}=50\%}\\\\\bullet \ \mathsf{\dfrac{2}{5}=40\%}[/tex]

[tex]\text{Now that we have that out the way. Let's solve for your answer!}[/tex]

[tex]\bf{\dfrac{1}{2}}\rightarrow\dfrac{2}{5}\rightarrow\dfrac{3}{10}}}} \leftarrow( that's\ for\ GREATEST\ to\ LEAST)[/tex]

[tex]\boxed{{\bf{Answer: \dfrac{1}{2}\ would\ be\ your\ GREATEST\ or \ BIGGEST\ one}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Evaluate the following expression.
-7+(63/9)

Answers

63 divided by 9 is 7, so -7+7 is 0

Hope this helped

Answer:

0

Step-by-step explanation:

using PEMDAS

63/9 = 7

-7 + 7 = 0

Between which two integers is the value of the square root of 20

Answers

Answer:

  4 and 5

Step-by-step explanation:

  20 is greater than 4² = 16, and less than 5² = 25. So, the square root of 20 is between 4 and 5.

___

Your calculator will tell you that √20 ≈ 4.472, so is between 4 and 5.

A flying disc has a circumference of 75.36 centimeters. What is the area of the flying disc? (Use 3.14 for .)

Answers

The area of flying disk is 452.16 square centimeters

Step-by-step explanation:

The disc is in circular shape so we will use the formulas for circle in this question.

Given

Circumference = C = 75.36 centimeters

We have to find the area of the disc for which we have to find the radius first.

Let r be the radius

Then

Circumference is given by:

[tex]C=2\pi r[/tex]

putting the values

[tex]75.36 = 2*3.14*r\\75.36 = 6.28r[/tex]

Dividing both sides by 6.28

[tex]\frac{6.28r}{6.28} = \frac{75.36}{6.28}\\r = 12\ cm[/tex]

The area of circle is given by:

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

Putting the values

[tex]A = 3.14 * (12)^2\\A = 3.14*144\\A =452.16\ cm^2[/tex]

Hence,

The area of flying disk is 452.16 square centimeters

Keywords: Circle, area

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What is the equation of the function that is graphed as line b?

y = 1/2 x - 1
y = 2x + 1
y = 1/2 x + 1
y = -4x

Answers

Following the slope of the line at x= 0 the line is at y =1 , at x=, it is at Y = 1.5, so the slope is 1/2

The y intercept is where the line crosses the y a is at x =0 which is 1

The equation would be y = 1/2x+ 1

Answer:

y = 1/2x+ 1

Step-by-step explanation:

Hey guys i need help please its slope and im struggling

Answers

Answer:

Slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].

Step-by-step explanation:

The slope of the line can be determined by simplifying the given equation to its standard form.

In the standard form, y =  mx + c, m represents the slope of the line.

We are given: [tex]$ y - 2 = - \frac{2}{3}(x + 1) $[/tex]

[tex]$ \implies y = -\frac{2}{3}x - \frac{2}{3} + 2 $[/tex]

[tex]$ \implies y = - \frac{2}{3}x + \frac{(-2 + 6)}{3} $[/tex]

[tex]$ \implies y = -\frac{2}{3}x + \frac{4}{3} $[/tex]

Comparing it with the standard equation, we can see that the slope, m = [tex]$ \frac{\textbf{-2}}{\textbf{3}} $[/tex].

Hence, the answer.

Angle x and angle y are complementary. angle x is supplementary to a 128 angle.What are the measures of angle x and angle y?

Answers

Answer:

y = 38°

Step-by-step explanation:

If Angle x and angle y are complementary, then x + y = 90°

Also, if angle x is supplementary to a 128 angle, then x + 128° = 180°.

Solving the latter equation for x, we get x = 52°.

Therefore, by the first equation, x + y = 90° becomes 52° + y = 90°, yielding

y = 38°

Answer:

[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]

[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to solve for the measures of angles x and y.}[/tex]

[tex]\textsf{First, x is supplementary to an angle that equals 128}^{\circ}.[/tex]

[tex]\Large\underline{\textsf{What are Supplementary Angles?}}[/tex]

[tex]\textsf{Supplementary angles are 2 or more angles that add up to \underline{180}}^{\circ}.[/tex]

[tex]\large\underline{\textsf{This means that;}}[/tex]

[tex]\mathtt{x+128^{\circ}=180^{\circ}.}[/tex]

[tex]\large\underline{\textsf{Subtract 128 from both sides for x:}}[/tex]

[tex]\boxed{\mathtt{x=52^{\circ}}}[/tex]

[tex]\Large\underline{\textsf{What are Complementary Angles?}}[/tex]

[tex]\textsf{Complementary angles are 2 or more angles that add up to \underline{90}}^{\circ}.[/tex]

[tex]\large\underline{\textsf{This means that;}}[/tex]

[tex]\mathtt{x+y=90^{\circ}.}[/tex]

[tex]\textsf{Because we know x, we can solve for y.}[/tex]

[tex]\large\underline{\textsf{Substitute:}}[/tex]

[tex]\mathtt{52^{\circ}+y=90^{\circ}.}[/tex]

[tex]\large\underline{\textsf{Subtract 52 from both sides for y:}}[/tex]

[tex]\boxed{\mathtt{y=38^{\circ}}}[/tex]

How do you calculate take-home pay?

Answers

The calculation of take home pay is the actual amount calculation of how much you will be credited on a job done well.

Step-by-step explanation:

Before calculation, things to be taken care of are -

Gross pay amountPersonal exemptionsTax statusDeductions of payroll

Now knowing these much in exact form of amount, we may proceed to calculation -

The annual income according to the gross pay amount is calculated by simply multiplying the gross pay amount to 12.The FICA tax percentage is known according to the tax slab of your annual income, so determine the FICA tax percent amount Other Personal Exemptions with Standard Deduction and Pay Roll Deductions are to be calculatedSum up all the taxable income and non taxable income separately, and deduct the amount of tax from the taxable income.The left over amount now shown is the annual income.Divide the annual income after the tax deduction by 12 to know the take home pay for monthly basis.

Write a function that represents the situation. Your $840 annual bonus increases by 5% each year

Answers

Answer:

[tex]f(x) = (840)\times (1.05)^{x}[/tex] where f(x) is the bonus every year and x is in number of years

Step-by-step explanation:

The function that represents the situation where $840 annual bonus increases by 5% each year is given by

[tex]f(x) = (840)\times (1.05)^{x}[/tex] where f(x) is the bonus every year and x is in number of years

Final answer:

The function representing an $840 annual bonus that increases by 5% each year is f(x) = 840(1 + 0.05)ˣ

Explanation:

To write a function that represents the situation where an $840 annual bonus increases by 5% each year, we can use an exponential growth model.

The general form of an exponential growth function is f(x) = a(1 + r)ˣ, where a is the initial amount, r is the growth rate, and x is the number of time periods.

In this case, the initial bonus a is $840, the growth rate r is 5% or 0.05, and x represents the number of years. Thus, the function can be written as:

f(x) = 840(1 + 0.05)ˣ

Help! Prove the equality

arccos √(2/3) - arccos (1+√6)/(2*√3) = π/6

Answers

Answer:

Proof in the explanation

Step-by-step explanation:

Trigonometric Equalities

Those are expressions involving trigonometric functions which must be proven, generally working on only one side of the equality

For this particular equality, we'll use the following equation

[tex]\displaystyle cos(x-y)=cos\ x\ cos\ y+sin\ x\ sin\ y[/tex]

The equality we want to prove is  

[tex]\displaystyle arccos\ \sqrt{\frac{2}{3}}-arccos\left(\frac{1+\sqrt{6}}{2\sqrt{3}}\right)=\frac{\pi}{6}[/tex]  

Let's set the following variables:

[tex]\displaystyle x=arccos\ \sqrt{\frac{2}{3}},\ y=arccos(\frac{1+\sqrt{6}}{2\sqrt{3}})[/tex]

And modify the first variable:

[tex]\displaystyle x=arccos\ \frac{\sqrt{6}}{3}}=>\ cos\ x= \frac{\sqrt{6}}{3}}[/tex]

Now with the second variable

[tex]\displaystyle y=arccos\ \frac{1+\sqrt{6}}{2\sqrt{3}}=>cos\ y=\frac{1+\sqrt{6}}{2\sqrt{3}}=\frac{\sqrt{3}+3\sqrt{2}}{6}[/tex]

Knowing that

[tex]sin^2x+cos^2x=1[/tex]

We compute the other two trigonometric functions of X and Y

[tex]\displaystyle sin \ x=\sqrt{1-cos^2\ x}=\sqrt{1-(\frac{\sqrt{6}}{3})^2}=\sqrt{1-\frac{6}{9}}=\frac{\sqrt{3}}{3}[/tex]

[tex]\displaystyle sin\ y=\sqrt{1-cos^2y}=\sqrt{1-\frac{(\sqrt{3}+3\sqrt{2})^2}{36}}}[/tex]

[tex]\displaystyle sin\ y=\sqrt{\frac{36-(3+6\sqrt{6}+18)}{36}}=\sqrt{\frac{15-6\sqrt{6}}{36}}[/tex]

Computing

[tex]15-6\sqrt{6}=(3-\sqrt{6})^2[/tex]

Then

[tex]\displaystyle sin\ y=\frac{3-\sqrt{6}}{6}[/tex]

Now we replace all in the first equality:

[tex]\displaystyle cos(x-y)=\frac{\sqrt{6}}{3}.\frac{\sqrt{3}+3\sqrt{2}}{6}+\frac{\sqrt{3}}{3}.\frac{3-\sqrt{6}}{6}[/tex]

[tex]\displaystyle cos(x-y)=\frac{3\sqrt{2}+6\sqrt{3}}{18}+\frac{3\sqrt{3}-3\sqrt{2}}{18}[/tex]

[tex]\displaystyle cos(x-y)=\frac{9\sqrt{3}}{18}=\frac{\sqrt{3}}{2}=cos\ \pi/6[/tex]

Thus, proven  

in the right triangle shown, ∠B=60° and BC = 2√3

Answers

Question:

In the right triangle shown, ∠B=60° and BC = 2√3

How long is AB?

Answer exactly, using a radical if needed.

The image of the triangle is attached below:

Answer:

The length of AB is [tex]4\sqrt{3}[/tex]

Explanation:

It is given that ∠B = 60° and BC = [tex]2\sqrt{3}[/tex]

To determine the length of AB, we shall use the cosine formula.

Because the value of the angle and its adjacent side is given and AB is the hypotenuse, we shall substitute the value of angle and adjacent side in the formula to find the value of AB.

Thus, the formula for [tex]\cos \theta[/tex] is given by

[tex]\cos \theta=\frac{a d j}{h y p}[/tex]

Where [tex]\theta=60[/tex] and [tex]adj= 2\sqrt{3}[/tex] and [tex]hyp=x[/tex]

Substituting these values in the formula, we get,

[tex]\cos 60=\frac{2 \sqrt{3}}{x}[/tex]

Interchanging, we get,

[tex]x=\frac{2 \sqrt{3}}{\cos 60}[/tex]

The value of [tex]cos 60 =\frac{1}{2}[/tex]

Substituting, we get,

[tex]x=\frac{2 \sqrt{3}}{\frac{1}{2} }[/tex]

[tex]x=4\sqrt{3}[/tex]

Thus, the value of x is [tex]4\sqrt{3}[/tex]

Hence, the length of the hypotenuse AB is [tex]4\sqrt{3}[/tex]

Roderick's credit card company calculates a finance charge based upon a periodic rate of 1.2% on all unpaid balances. If Roderick has an unpaid balance of $200, determine the finance charge that he will be assessed. $301.80 $298.20 $2.40 $54.00

Answers

Answer:

  $2.40

Step-by-step explanation:

You have ...

  finance charge = 1.2% × unpaid balance

     = 0.012 × $200 . . . . . fill in the value of unpaid balance

  finance charge = $2.40

Given the sequence 2, 4, 8, , 16,........, where x = 0, 1, 2, 3, .......what is the function rule? f(x) = 2x + 2 f(x) = 2(2)x f(x) = (2x) f(x) = 2

Answers

f(x) = 2([tex]2^{x}[/tex])

Step-by-step explanation:

Step 1 :

Given

When  x =0, f(x) = 2

x =1, f(x) = 4

x =2, f(x) = 8

x =3, f(x) = 16

Step 2 :

Substituting for x in the function f(x) = 2([tex]2^{x}[/tex]) we get,

When  x =0, f(x) = 2

x =1, f(x) = 4

x =2, f(x) = 8

x =3, f(x) = 16

This matches the given sequence and this shows that the function represents the given sequence .

Final answer:

The function rule for the given sequence 2, 4, 8, 16, ... is [tex]f(x) = 2^x[/tex], representing the sequence's exponential growth pattern where each term is double the previous term.

Explanation:

The given sequence is 2, 4, 8, 16, ..., which is a geometric sequence where each term is multiplied by 2 to get the next term. This pattern corresponds to an exponential function where the base is 2 and the exponent is the position of the term, which can also be thought of as the function's input, x. Therefore, the function that represents this sequence is f(x) = 2x.

The other function choices given, such as f(x) = 2x + 2 or f(x) = 2, do not correctly represent the pattern observed in the sequence. The correct function rule for the given sequence is f(x) = 2x which fits the pattern where when x is substituted for each term's position (starting from 0), the function provides the corresponding term of the sequence.

How do you solve the system of the linear equation by substitution?
y=x-4
4x-y=3

Answers

Answer:

x=-1/3, y=-13/3. (-1/3, -13/3).

Step-by-step explanation:

y=x-4

4x-y=3

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

4x-(x-4)=3

4x-x+4=3

3x+4=3

3x=3-4

3x=-1

x=-1/3

y=-1/3-4

y=-1/3-12/3=-13/3

Answer: ([tex]-\frac{1}{3},-\frac{13}{3}[/tex]

Step-by-step explanation:

Substitut (x-4) into the equation of 4x-y=3

(Substitute what y equals into the equation

Make sure to keep parentheses!

That becomes 4x-(x-4)=3

Than you must distribute the negative to x and to -4

When you do it creates the equation of 4x-x+4=3

When combining like terms you get: 3x+4=3

Then solve                                                -4   -4

3x=-1

3    3               x=-1    

                           3

Than substitute the x in for the equation of y=x-4 to find what y equals! since you know that x equals -1/3 than subtract -1/3 - 4 to get

y= -13          

     3        

What is the value of the expression when n = 3?

StartFraction 6 (n squared plus 2) Over n EndFraction

Answers

The value of expression when n = 3 is 22

Solution:

Given expression is:

[tex]\frac{6(n^2 + 2)}{n}[/tex]

We have to find the value of expression when n = 3

Substitute n = 3 in given expression

[tex]\rightarrow \frac{6(3^2 + 2)}{3}\\\\Simplify\ the\ above\ expression\\\\\rightarrow \frac{6(9+2)}{3}\\\\Solve\ the\ terms\ inside\ the\ bracket\\\\\rightarrow \frac{6(11)}{3}\\\\Divide\ 6\ by\ 3 \\\\\rightarrow 2 \times 11 = 22[/tex]

Thus the value of expression when n = 3 is 22

Answer:

22

Step-by-step explanation:

How do you write 3x+4y=12 in slope-intercept form?

Answers

Answer:

y=-3/4x+3

Step-by-step explanation:

3x+4y=12

4y=12-3x

4y=-3x+12

y=-3/4x+12/4

y=-3/4x+3

Which products result in a difference of squares or a perfect square trinomial? Check all that apply.
(5x + 3)(5x - 3)
(7x + 4)(7x + 4)
(2x + 1)(x + 2)
(4x – 6)(x + 8)
(x – 9)(x – 9)
(-3x - 6)(-3x + 6)

Answers

All you need to do is convert all equations into standard form by using the distributive property on each equation.

Answer:

A (5x + 3)(5x – 3)

B (7x + 4)(7x + 4)

E (x – 9)(x – 9)  

F (–3x – 6)(–3x + 6)

in other words, A,B,E, and F on edge-nuity. just completed with 100%

Step-by-step explanation:

two sepp equtions with intgefs
9+m/3=2
slove

Answers

Answer: [tex]m=-21[/tex]

Step-by-step explanation:

In order to solve the exercise, you need to remember the following properties:

1. Addition property of equality:

If [tex]a=b[/tex], then [tex]a+c=b+c[/tex]

2. Subtraction property of equality:

If [tex]a=b[/tex], then [tex]a-c=b-c[/tex]

3. Divison property of equality:

If [tex]a=b[/tex], then [tex]\frac{a}{c}=\frac{b}{c}[/tex]

4. Multiplication property of equality:

If [tex]a=b[/tex], then [tex]a*c=b*c[/tex]

Then, given the following equation:

[tex]9+\frac{m}{3}=2[/tex]

You need to followw these steps in order solve for "m":

- Apply the Subtraction property of equality subtracting 9 from both sides of the equation:

[tex]9+\frac{m}{3}-9=2-9\\\\\frac{m}{3}=-7[/tex]

- Apply the Multiplication property of equality multiplying both sides of the equation by 3. Then, you get:

[tex](3)(\frac{m}{3})=(-7)(3)\\\\m=-21[/tex]

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