Find the value of x

Area of rectangle = 50

Answer:

Step-by-step explanation:

A hypotenuse is calculated on a triangle with a right angle. The hypotenuse is the side opposite the sides with the right angle. The equation is a^2 + b^2=c^2 where the hypotenuse is the square root of c.

The length of the segment CB in triangle ABC where \(\overline{AM}\) is a median line and CM = 5·x - 2, MB = 3·x + 12, CM = MB, is 66 units

A median line is a line that is drawn from a vertex of a triangle to the middle of the opposite side such that the it bisects the opposite side.

The parameters are; \(\overline{AM}\) = A median line

Length of segment CM = 5·x - 2

Length of segment MB = 3·x + 12

Required; The length of segment CB

The median line \(\overline{AM}\) bisects the segment CB

Therefore; CM = MB

CB = CM + MB (Angle addition postulate)

Which gives; 5·x - 2 = 3·x + 12 (substitution property of equality)

2·x = 14

x = 14 ÷ 2 = 7

CB = CM + MB

CB = (5·x - 2) + (3·x + 12)

Which gives; CB = 8·x + 10

x = 7

CB = 8×7 + 10 = 66

The length of segment CB =  66

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Answer:

S₇ = 514.75

Step-by-step explanation:

the nth term of a geometric sequence is

\(t_{n}\) = a\(r^{n-1}\)

where a is the first term and r the common ratio

given t₂ = 24 and t₅ = 81 , then

ar = 24 → (1)

a\(r^{4}\) = 81 → (2)

divide (2) by (1) to eliminate a

\(\frac{ar^{4} }{ar}\) = \(\frac{81}{24}\)

r³ = \(\frac{81}{24}\) ( take cube root of both sides )

\(\sqrt[3]{r^{3} }\) = \(\sqrt[3]{\frac{81}{24} }\)

r = 1.5

substitute r = 1.5 into (1) and solve for a

a × 1.5 = 24 ( divide both sides by 1.5 )

a = 16

the sum to n terms of a geometric sequence is

\(S_{n}\) = \(\frac{a(r^{n}-1) }{r-1}\) , then

S₇    = \(\frac{16((1.5)^{7}-1)) }{1.5-1}\)

      = \(\frac{16(17.0859375-1)}{1.5-1}\)

     = \(\frac{16(16.0859375)}{0.5}\) ( divide 16 by 0.5 )

     = 32 × 16.0859375

     = 514.75

Answer:

The second box plot represents the data

Step-by-step explanation:

A box and whisker plot gives you the five-number summary of the data, which includes:

the minimum (lowest value of the data)

the maximum (highest value of the data)

Q1 (25% of the data lies below this point)

Q3 (75% of the data lies below this point), and

the median (the middle of the data).

The two ticks at the far left and far right of the box-and-whisker plot are the minimum and maximum respectively.  From the data, we see that the minimum is 5 and the maximum is 10.

Although both plots have a minimum value of 5, only the second plot has the accurate maximum at 10.

Assets are the goods you possess that can generate future economic advantage. The correct option is D.

Assets are the goods you possess that can generate future economic advantage. Liabilities are amounts owed to other parties. In a nutshell, assets put money in your pocket, while liabilities take money out!

Given Over the period of a year, Julie’s net worth decreased. Therefore, the statement that is true is Julie’s assets decreased by more than her liabilities.

Hence, the correct option is D.

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Given statement solution is :- If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

If the expression 12x - 6x + 5 + 4x is set equal to 10x + 5, then there would be solution(s).

If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

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9514 1404 393

Answer:

  A: 8x +24

  B: not equivalent for any value of x

Step-by-step explanation:

Part A:

The factor of 4 on the outside of parentheses multiplies each term inside:

  M = 4(2x) +4(6)

  M = 8x +24 . . . . . expression equivalent to M

__

Part B:

Expressions M and N are not equivalent for any value of x. They are equivalent if their difference is zero or can be made to be zero. Subtracting N from M, we find the difference to be ...

  M -N = (8x +24) -(8x +10) = 14

There is no value of x that will make the difference of 14 become zero.

The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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Answer:

D. A cant be a factor of the polynomial because the highest degree is 4. Since the polynomial cant be factored any more after (4x^2)*(3(x^2)-5x+1), D is the answer

Answer:

D

Step-by-step explanation:

12\(x^{4}\) - 20x³ + 4x² ← factor out 4x² from each term

= 4x²(3x² - 5x + 1) ← in factored form

with one factor 3x² - 5x + 1

Answer:

\(A=301.593\ cm^3\)

Step-by-step explanation:

The Surface Area of a Cylinder

Given a cylinder of base radius r and height h, the surface area is calculated (including the top and bottom areas):

\(A = 2\pi r^2+2\pi r h\)

The cylinder has a height of h=8 cm and a radius of r=4 cm. Substituting:

\(A = 2\pi 4^2+2\pi *4*8\)

\(A = 32\pi +64\pi\)

\(A=96\pi\)

Calculating

\(\boxed{A=301.593\ cm^3}\)

Answer: 301.593 cm2

Step-by-step explanation:

Answer:

x = 24

Step-by-step explanation:

Step 1:

5x -3 + 2x + 15 = 180

Step 2:

7x + 12 = 180

Step 3:

7x = 168

Answer:

x = 24

Hope This Helps :)

Answer:

7

Step-by-step explanation:

170/25

170 divided by 25

= 6.8

round it up to 7

The exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

An exponential function is represented as:

\(y = b^x\)

The base is 3.

So, we have:

\(y = 3^x\)

It is stretched vertically by 2/3.

So, we have:

\(y = \frac23(3)^x\)

When reflected over the y-axis, we have:

\(y = \frac23(3)^{-x}\)

An asymptote of y = 2, makes the function becomes

\(y = \frac23(3)^{-x} + 2\)

Lastly, it passes through the point (0, 3.5).

So, we have:

\(y = \frac23(3)^{-x+h} + 2\)

This gives

\(3.5 = \frac23(3)^{-0+h} + 2\)

\(3.5 = \frac23(3)^{h} + 2\)

Subtract 2 from both sides

\(1.5 = \frac23(3)^{h}\)

Multiply by 3/2

\(2.25 = (3)^{h}\)

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in \(y = \frac23(3)^{-x+h} + 2\)

\(y = \frac23(3)^{-x+0.74} + 2\)

Hence, the exponential equation is \(y = \frac23(3)^{-x+0.74} + 2\)

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The sale price for the snowboard after the trade and loyalty discount of 15% and 4% will be 351.01 dollars.

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 ‘%’.

Frigid Boards purchases one of its snowboards for $395 less a retail trade discount of 15% and a loyalty discount of 4%. Then the price of the snowboards will be

⇒ $ 395 × 0.85 × 0.96

⇒ $ 322.32

Its markup on selling price percentage on all snowboards is 21%, then we have

⇒ $ 322.32 × 1.21

⇒ $ 390.01

At the end of the season, any leftover snowboards are marked down by 10%, then we have

⇒ $ 390.01 × 0.90

⇒ $ 351.01

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60 is thaks for points

Step-by-step explanation:

I think

The Product of 1 5/8, 2, and 3/5 is equal to 39/20, which is simplified completely. The answer is 39/20.

To find the product and simplify completely, you need to perform multiplication and simplify the resulting fraction. Here, we are multiplying the following fractions and mixed numbers:1, 5/8, 2, and 3/5.The first step is to convert the mixed numbers into improper fractions.

We do that by multiplying the whole number by the denominator, and then adding the numerator.For 1 5/8, we get:$$1 \frac{5}{8} = \frac{8}{8} \times 1 + \frac{5}{8} = \frac{13}{8}$$For 2, we get:$$2 = \frac{2}{1} = 2 \times \frac{1}{1} = \frac{2}{1}$$For 3/5, we leave it as is since it's already a fraction.

Now that we have all the numbers as fractions, we can multiply them:$$\frac{13}{8} \times \frac{2}{1} \times \frac{3}{5} = \frac{13 \times 2 \times 3}{8 \times 1 \times 5} = \frac{78}{40}$$

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 2:$$\frac{78}{40} = \frac{2 \times 39}{2 \times 20} = \frac{39}{20}$$

Therefore, the product of 1 5/8, 2, and 3/5 is equal to 39/20, which is simplified completely. The answer is 39/20.

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The third side of the triangle 12.5

A triangle is a polygon with three edges and three vertices. The important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

we the measurements of given two sides of the triangle 16.5 and 29

In a triangle, the sum of any two sides should be greater than the third side and the difference between any two sides should be lesser than that of the third side.

The sum of two sides rule

\(x + 16.5 > 29\\ x > 29 - 16.5\\ x > 12.5\\\)

The difference between the two sides rule

\(29 - 16.5 < x \\ 12.5 < x\)

Therefore, the value of x is 12.5

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Answer:

y= -1/2(x) +8

gradient= -1/2

Intercept= 8

Step-by-step explanation:

Let's transform the equation to y -intercept form first

6x - 3y - 15= 0

-3y= -6x+15

Y= -6/-3(x) +(15/-3)

Y= 2x -5

Intercept c= -5

Gradient m =2

Rule of perpendicularity

mm'= -1

m'= -1/m

m' = -1/2

Equation of line of the point (4, 6)

(Y-Y1)/(x-x1)=m'

(Y-6)/(x-4)= -1/2

2(y-6)= -1(x-4)

2y -12 = -x +4

2y= -x +4+12

2y= -x+16

y= -1/2(x) +8

gradient= -1/2

Intercept= 8

Answer:

(48, 3), (80, 5), (160, 10)

The solution of the trigonometric equation sec²θ = 2tanθ is θ = π/4 or 5π/4

A trigonometric equation is an equation that contains the trigonometric ratios.

Given that  sec²θ = 2tanθ.

We solve the trigonometric equation as follows

sec²θ = 2tanθ.

We know that the trigonometric identity tan²θ + 1 = sec²θ

Substituting this into the equation, we have that

sec²θ = 2tanθ.

tan²θ + 1 = 2tanθ.

Re-arranging the equation, we have that

tan²θ - 2tanθ + 1 = 0

Factorizing, we have that

tan²θ - tanθ - tanθ + 1 = 0

tanθ(tanθ - 1) - (tanθ - 1) = 0

(tanθ - 1)(tanθ - 1) = 0

(tanθ - 1)² = 0

(tanθ - 1) = 0

tanθ = 1  (twice)

Taking inverse tan of both sides, we have

θ = tan⁻¹(1)

= π/4 or π +  π/4

= π/4 or 5π/4

So, the solution is θ = π/4 or 5π/4.

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Answer:

Step-by-step explanation:

Direction: Opens Up

Vertex:

(

0.784

¯¯¯¯

09

,

551.69488

¯¯¯¯

63

)

Focus:

(

0.784

¯¯¯¯

09

,

551.75170

¯¯¯¯

45

)

Axis of Symmetry:

x

=

0.784

¯¯¯¯

09

Directrix:

y

=

551.63806

¯¯¯¯

81

Select a few

x values, and plug them into the equation to find the corresponding

y values. The

x values should be selected around the vertex.

Replace the variable

x

with

0

in the expression.

f

(

0

)

=

4.4

(

0

)

2

−

6.9

⋅

0

+

554.4

Simplify the result.

Tap for more steps...

554.4

The

y

value at

x

=

0

is

554.4

.

y

=

554.4

Replace the variable

x

with

−

1

in the expression.

f

(

−

1

)

=

4.4

(

−

1

)

2

−

6.9

⋅

−

1

+

554.4

Simplify the result.

Answer:

2/11

Step-by-step explanation:

6/11 x 1/3 =

6/33 =

2/11

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

2/11 as a fraction

0.18 as a decimal

Step-by-step explanation:

The equation of the Parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2

The vertex form of a parabola is given by:y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

We are given that the vertex is (4, -2), so we can substitute these values in the equation to get:y = a(x - 4)^2 - 2

Now, we need to find the value of "a". To do this, we can use the fact that the y-intercept is (0, -66). Since the point (0, -66) lies on the parabola, we can substitute x = 0 and y = -66 in the equation above to get:-66 = a(0 - 4)^2 - 2

Simplifying this, we get:-66 = 16a - 2

Adding 2 to both sides, we get:-64 = 16a

Dividing both sides by 16, we get:a = -4

Substituting this value of "a" in the equation above, we get the equation of the parabola in vertex form:y = -4(x - 4)^2 - 2

Therefore, the equation of the parabola in vertex form that has a vertex of (4, -2) and a y-intercept of (0, -66) is:y = -4(x - 4)^2 - 2

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Answer: 127^9 so 8594754748609400000

Step-by-step explanation: i’m not sure but 4+6 (7x3)-3 = 127 127^9

The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

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Answer:

\(x=10\)

Step-by-step explanation:

Set up a proportion with corresponding sides. The two sides marked with a small line in them represent that those sides are equal. Therefore, the side marked 30 is broken into two lines of equal length (each 15).

Thus, we can set up the following proportion:

\(\frac{x}{20}=\frac{15}{30},\\\\30x=300,\\\\x=\boxed{10}\)

Answer:

8 years is around 2,920 days

Step-by-step explanation:

Answer: 2920 days

Step-by-step explanation:

1 year = 365 days

8 years = ?

8 years x 365 days = 2920 days

The least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

The equation in this problem is given as follows:

1/x + 2/(x - 3) = 5.

The denominators of each expression are given as follows:

x and x - 3 are not factors of each other, hence we multiply them and the least common denominator needed to solve the equation is given as follows:

D. x(x - 3).

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