He sold a car for 247,250 at a profit of 15%, what was the price of the car?

(A) (4,0), (D) (0, -5), and (E)(2, -5/2) are the solutions of the given equation 5x – 4y = 20.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

The typical form for linear equations with two variables is Ax+By=C.

For instance, the linear equation 2x+3y=5 is in standard form.

So, we have the equation:

5x – 4y = 20

(A) (4,0)

=5x−4y

=5(4)−4(0)

=20

=RHS

(4,0): YES

(B) (0,5)

=5x−4y

=5(0)−4(5)

=−20

≠RHS

(0,5): NO

(C) (−2, 5/2)

=5x−4y

=5(−2)−4(5/2)

=−10−10

=−20

(−2, 5/2): NO

(D) (0, -5)

=5x−4y

=5(0)−4(−5)

=20

=RHS

(0, -5): YES

(E) (2, -5/2)

=5x−4y

=5(2)-4(-5/2)

=10+10

=20

=RHS

(2, -5/2): YES

Therefore, (A) (4,0), (D) (0, -5), and (E)(2, -5/2) are the solutions of the given equation 5x – 4y = 20.

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Answer:

96 dollars

Step-by-step explanation:

The ratio of Miguel's savings to his earnings is 8: 10 = 40: 50 = 120: 150 is equal to ratio 4:5

If Miguel earns $120, then he will save 4/5 of his earnings.

This can be expressed as a ratio as follows:

Savings: Earnings = 4 : 5

This means that for every 4 units of savings, there are 5 units of earnings. In other words, the ratio of savings to earnings is 4 to 5.

In order to calculate the amount of money that Miguel will save; we can multiply the ratio by the amount of earnings.

In this case, the amount of earnings is $120, so the amount of money that Miguel will save is:

[tex]\textsf{Savings} =\dfrac{ 4}{5 }* 120 = 96[/tex] dollars

Therefore, He will save 96 dollars if he earns 120 dollars.

Answer:

y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{41}{5}[/tex]

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 )

y = [tex]\frac{5}{4}[/tex] x - 1 ← is in slope- intercept form

with slope m = [tex]\frac{5}{4}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex] , then

y = - [tex]\frac{4}{5}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (4, 5 ) into the partial equation

5 = - [tex]\frac{16}{5}[/tex] + c ⇒ c = 5 + [tex]\frac{16}{5}[/tex] = [tex]\frac{25}{5}[/tex] + [tex]\frac{16}{5}[/tex] = [tex]\frac{41}{5}[/tex]

y = - [tex]\frac{4}{5}[/tex] x + [tex]\frac{41}{5}[/tex] ← equation of perpendicular line

Answer:

(D)

Step-by-step explanation:

This is because if you have 3 angles, there is an infinite amount of possible triangles. For example, if you have a triangle with the angles 30 degrees, 60 degrees, and 90 degrees, you could have any triangle with side ratios of 1:[tex]\sqrt{3}[/tex]:2.

The term that describes measures that would be taken to decrease the size of a professional sports is contraction.

Contraction is the act of decreasing or drawing collectively to make smaller; the alternative of expansion. In this case, the proprietors need to lessen the wide variety of groups with the aid of using removing franchises which are dropping the maximum money. Players who're on Minor League or break up contracts aren't completely assured their salaries. A participant on a break up or Minor League settlement will earn the prorated part of his Major League earnings for time spent at the Major League roster.

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Proof of  angle 6 is congruent to angle 4 is given.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Angles of equal measure are said to have congruent angles.

Given,

∠1 ≅ ∠3

And we know from the vertical angles, property;

The angles opposite each other when two lines cross.

They are always equal.

And here we have two pairs of vertical angles,

So, ∠1 = ∠4

and ∠3 = ∠6

And ∠1 ≅ ∠3 is given.

So,  ∠1 ≅ ∠4

and ∠3 ≅ ∠6

Comparing, we get

∠4 ≅ ∠6

Therefore, ∠4 ≅ ∠6 is proved.

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C. Albino alligators are very rare.

What is crocodiles ?

Crocodiles are large reptiles found in tropical regions of Africa, Asia, the Americas and Australia. They are members of the order Crocodilia, which also includes caimans, gharials and alligators.

crocodiles are more than alligators in the reptile tent because Albino alligators are very rare. according to the passage there are more types of crocodiles ans less alligators.

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The company's cost of preferred stock is 9.08%, which means the correct answer is B) 9.08%. The cost of a service may be determined by the amount of time and expertise required to provide it. In general, cost is an important factor in determining the feasibility and profitability of a project or business venture.

Cost refers to the amount of money that is required to purchase or produce something. For example, the cost of a product may be determined by the amount of materials and labor that went into producing it, as well as any other expenses associated with bringing it to market.

To calculate the company's cost of preferred stock, we need to use the following formula:

Cost of preferred stock = annual dividend / price per share - flotation cost

In this case, the annual dividend is $8.50, the price per share is $97.50, and the flotation cost is 4.00% of the price paid by investors. Plugging these values into the formula, we get:

Cost of preferred stock = $8.50 / $97.50 - 4.00% = $8.50 / $97.50 * (1 - 0.04) = $8.50 / $93.80 = 0.0908

Therefore, the company's cost of preferred stock is 9.08%, which means the correct answer is B) 9.08%.

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The equation of line passes through the points (14, 10) and (0, 2) will be;

⇒ y = 4/7x + 2

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (14, 10) and (0, 2)

Now,

Since, The equation of line passes through the points (14, 10) and (0, 2)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (2 - 10) / (0 - 14)

m = - 8 / - 14

m = 4/7

Thus, The equation of line with slope 4/7 is,

⇒ y - 10 = 4/7 (x - 14)

⇒ y - 10 = 4/7 (x - 14)

⇒ y = 4/7x - 8 + 10

⇒ y = 4/7x + 2

Therefore, The equation of line passes through the points (14, 10) and

(0, 2) will be;

⇒ y = 4/7x + 2

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Answer:

1/ $ 4.08

2/ $675.92

Step-by-step explanation:

Take 68 times 0.06% = $4.08

680 - 4.08= 675.92

Answer:

Step-by-step explanation:

40.80 it told me the answer

The sample mean is less than 26.92 hours per week .

What is  standard deviation?

Your dataset's average level of variability is represented by the standard deviation. In general, it reveals how far away from the mean each value is.

                  A low standard deviation denotes that values are grouped closely to the mean, while a high standard deviation denotes that values are typically spread widely from the mean.

Let X~ Normal (26, 4/√16) distribution ie Normal (26, 1) distribution

We want,

P(X<a) = 0.82

Using standard normal approximation,

P(z< (a-26)/1) = 0.82

Using standard normal distribution tables, we get

(a-26)/1 = 0.915

(Since P(z<0.915) = 0.82)

So, a= 26+0.915= 26.915

So the required value is 26.92 (rounded to two decimals)

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The coordinates of the y-intercept is (0, 10)

The coordinate of the x-intercept is (5 / 2, 0)

Cynthia is participating in the Spartan Super, a 10-mile obstacle course.  She completes 4 miles of the obstacle course every hour.

Cynthia’s distance from this finish line, y, after x hours is represented by the function 4x + y = 10.

Therefore, the y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when x = 0.

The x-intercept is where a line crosses the x-axis. The x-intercept is the value of x when y = 0.

Linear function in slope intercept form is as follows:

y = mx + b

where

Hence,

4x + y = 10

y = -4x + 10

Hence, y-intercept is 10.

y = -4x + 10

Let's find x-intercept

0 = -4x + 10

-10 = -4x

x = 10 / 4

x = 5 / 2

x-intercept is 5 / 2.

Hence the coordinate of the y-intercept is (0, 10) and the x-intercept is (5 / 2, 0)

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Answer:

Step-by-step explanation:

There a few ways to solve this system. Since each equation is set equal to y on the left side, that means that we can set the right side of each equation to be equal to each other. So,

3x - 4 = -2x + 6

This can now be solved for x:

5x - 4 = 6 (added 2x to each side)

5x = 10 (added 4 to each side)

x = 2 (divided each side by 5)

Now that we know what x must be, we can plug 5 in for x in either of the equations and solve for y:

y = 3(5) - 4

y = 6 -4

y=2

This means y should be 2. To make sure this answer is correct, we can plug our y and x numbers into the OTHER equation to see if it makes sense:

(2) = -2(2) + 6

2 = -4 + 6

2=2

That looks right, so x = 2 and y = 2

There are Three months in a quarter of a year.

To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:

1 year = 4 quarters

1 quarter= [tex]\frac{1}{4}[/tex] year

1 year = 12 months

Thus,

1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)

1 quarter = [tex]\frac{12}{4}=3[/tex]

So, There are Three months in a quarter of a year.

One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).

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There are Three months in a quarter of a year.

To determine what is being asked, divide the total number by the denominator and get the portion using the numerator:

1 year = 4 quarters

1 quarter= [tex]\frac{1}{4}[/tex] year

1 year = 12 months

Thus,

1 quarter = (Total number of months in year) ÷ (Total number of quarters in a year)

1 quarter = [tex]\frac{12}{4} =3[/tex]

So, There are Three months in a quarter of a year.

One year typically refers to a period of 365 days or 12 months. It usually includes the entire calendar year from January 1st to December 31st. It can also refer to a fiscal year (a period of 12 consecutive months used for accounting purposes) or a school year (which may start in late summer).

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Answer: 6 boxes of 5 markers in each box

Step-by-step explanation:

1. Consider the factors of 30

30: 1, 2, 3, 5, 6, 10, 15 and 30

2. pick any 2 that make 30

5*6=30

3. Therefore buying 6 boxes of 5 markers each should do the trick,

Hope this helps

Answer: 6 boxes of 5 markers in each box

Step-by-step explanation:

The rowing team's speed in still water is 6 miles per hours for 6 hours 15 minutes.

Given that,

In the same time it took to row 25 miles against the current, a rowing team was able to row 50 miles while travelling with it. 2 miles per hour was the current's speed.

We have to calculate the rowing team's speed in still water.

We know that,

Let rowing rate in still water = r

And current rate = c = 2 mph

Rowing with the current means the overall speed is r + c = r + 2

Rowing against the current means the overall speed is r - c = r - 2

Distance = Rate × Time

50 = (r+2) × t  ----->equation(1)  

25 = (r-2) × t  ----->equation(2)

By solving

Divide equation(1) by equation(2)

50/25 = (r+2) × t / (r-2) × t

2=r+2/r-2

2(r-2)=r+2

2r-4=r+2

2r-r=2+4

r=6mph

Substitute in equation(1)

50 = (r+2) × t

50=(6+2)×t

50=8t

t=50/8

t=6.25 hrs

t= 6 hours 15 minutes

Therefore, the rowing team's speed in still water is 6 miles per hours for 6 hours 15 minutes.

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Answer:             5

Step-by-step explanation: because

The matrices A and B are not inverse matrices

From the question, we have the following parameters that can be used in our computation:

[tex]A = \left[\begin{array}{cc}-2&-3&2&-2\end{array}\right][/tex]

[tex]B = \left[\begin{array}{cc}1&-1&-1&2\end{array}\right][/tex]

To determine if the matrices are inverse matrices, we simply calculate the inverse of matrix A and then make the comparison.

The matrix A is given as

[tex]A = \left[\begin{array}{cc}-2&-3&2&-2\end{array}\right][/tex]

Calculate the determinant of the matrix A

So, we have the following representation

|A| = -2 * -2 + 3 * 2

Evaluate the sum of products

|A| = 10

The inverse is then calculated as

[tex]A^{-1} = \frac 1{10} * \left[\begin{array}{cc}-2&3&-2&-2\end{array}\right][/tex]

Evaluate

[tex]A^{-1} = \left[\begin{array}{cc}-\frac 1{5}&\frac 3{10}&-\frac 1{5}&-\frac 1{5}\end{array}\right][/tex]

When compared to matrix B, both matrices are different

Hence, the matrices are not inverse matrices

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Answer:

6 7/12

Step-by-step explanation:

"12 1/4 - 5 2/3" is an expression.  It is not said to equal anything.  The "=" sign makes it an equation.  But we can evalute an expression by simplyfying it.  Let's do the subtraction.  We first need to convert one of the fractions so that it has the same denominator as the other.

12 1/4 - 5 2/3 can be written as (12 - 5)+(1/4 - 2/3)

(12 - 5)+(1/4 - 2/3)

(7)+(1/4 - 2/3)        Let's convert both fractions to have denominators of 12 [since 4*3 = 12]

7 + 1/4 - 2/3

7 + (1/4)*(3/3) - (2/3)*(4/4)   [Multiply the tqo fractions by (3/3) and (4/4), repectively.  This is OK since both are the equivalent of multiply by 1.  But it converts the denominators so that we can now add or subtract.

7 + (3/12) - (8/12)

7 - (5/12)

or 6 7/12

Answer:

Questions and answers

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Question

The perimeter of a shape is 25.71 cm calculate the value of the radius X takes pie to be 3.142

Answer · 15 votes

Answer:5 cmStep-by-step explanation:Given a semicircle with perimeter 25.71 cm, we are required to find the radius of the circle.Circumference of a Semicircle=Length of the Circular part+Length of the diameter[tex]=\pi r+2r[/tex][tex]If \: \pi=3.142, C=25.71\Then:\25.71=3.142r+2r (3.142+2)=25.71\5.142r=25.71 =25.71 \div5.142 =5cm[/tex]

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Question

The perimeter of the semicircle is 25.71 cm. Calculate the value

Answer:

Step-by-step explanation  you add the 25.50 +2.50=27.00

and then add 115 to it 143.00

The volume of an object is  length × width × height.

What is three dimension geometrical shape?

3D forms are three-dimensional solid shapes or figures in geometry. Typically, the dimensions of 3D objects are length, breadth, and height. These shapes are known by the common names cube, cuboid, cone, cylinder, and sphere. The characteristics of 3D shapes, such as their edges, faces, vertices, curved surfaces, lateral surfaces, and volumes, determine what they are.

In our daily lives, we encounter many items of all sizes and shapes. Golf balls, doormats, ice cream cones, Coke cans, and other items are available. The various 3D shapes, surface area, and volumes, as well as the method of creating 3D shapes utilizing nets with the aid of 2D Shapes, will all be covered in this article.

A rectangular prism's volume can be calculated by multiplying its base area by its height. A rectangular prism's area will be l × w since its base is also a rectangle. The volume of the prism is then calculated by multiplying this area by the prism's height. As a result, another method to construct this formula is to multiply the prism's length, breadth, and height and then convert the result to cubic units.

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Answer:

the first number is 20, second is 9

Step-by-step explanation:

y=3x-7

y+x=29

rearrange the first equation

y-3x=-7

and

y+x=29

solving the simultaneous equation:

y-3x=-7

            -

y+x=29

= -4x=-36

divide both sides by -4

x = 9

now substitute the x value into the equation: y+x=29

= y + 9 = 29

y = 20

Fundamental theorem of arithmetic states that each positive integer n is greater than 1 represented by unique set of prime numbers.

Explanation:

Fundamental theorem of arithmetic states that all the positive integer n is greater than 1 represented by multiples of prime numbers or the number itself is a prime number.

For example :

Let us consider 56 be a integer greater than 1

56 = 2 × 2 × 2 × 7

2 and 7 both are prime numbers

another example :

29 = 29 × 1

29 itself is a prime number.

Factorization of the given numbers itself prove the fundamental theorem of arithmetic.

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Solving the given equations using substitution method we get (x,y) as (2, -1) i.e option (2) is correct answer.

Substitution method

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

Given: 4x + 2y = 6      --------- (1)

            x = 2y + 4        ----------(2)      

Put the value of x from the 2nd equation in the 1st equation

4(2y+4) +2y = 6

8y + 16 + 2y = 6

10y + 16 = 6

10y = 6-16

10y = -10

y = -1 --------------- (3)

put the value of y in the (2) from (3)

x = 2(-1) + 4

x = -2+4

x = 2

Therefore, its solution is (2, -1)

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Answer: B

Step-by-step explanation: Did the test

Answer: y=—2/3x+2

Step-by-step explanation:

On solving the provided question, we have the followings roots of the equations as -  x3 - 23x2 + 142x - 120 = (x - 1) (x - 10) (x - 12) and (x-1)(x-2)(x-3)=0

f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are real integers and a 0. The cubic function is the cubic polynomial function. The higher cube function, or the fundamental cubic function, is defined as f(x) = x3.

x3 – 6x2 + 11x – 6 = 0.

(x-1)(x-2)(x-3)=0

x3 – 23x2 + 142x – 120.

first factorize

[tex]x3 - 23x2 + 142x - 120 = (x - 1) (x2 - 22x + 120)\\ But x2 - 22x + 120 = x2 - 12x - 10x + 120\\ = x (x - 12) -10(x - 12)\\ = (x - 12) (x - 10)\\ Therefore,\\ x3 - 23x2 + 142x - 120 = (x - 1) (x - 10) (x - 12)[/tex]

Equate each factor to zero to get;

x = 1

x = 10

x = 12

The roots of the equation are x = 1, 10 and 12.

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The length of the Hypotenuse for the given right angle triangle, is 10√5.

What is Hypotenuse?

A right-angled triangle's longest side, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem states that the hypotenuse's square length equals the sum of the squares of the lengths of the other two sides, and this can be used to determine the hypotenuse's length.

Let the two sides of right angle triangle are, a = 20 and b = 10.

We have to find the length of Hypotenuse.

Let x be the length of Hypotenuse.

So, by using the Pythagoras theorem,

[tex]a^2 + b^2 = x^2[/tex]

Plug a = 20, b = 10

[tex](20)^2 + (10)^2 = x^2\\400 + 100 = x^2\\500 = x^2\\x^2 = 500\\x = 10\sqrt{5}[/tex]

hence, the length of the Hypotenuse for the given right angle triangle, is 10√5.

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Using the area of the rectangle, we know that the length of the given rectangle is x + 9.

The area is described as the amount of space occupied by a flat (2-D) surface or shape of an object.

Take a marker pen and attract a square on a bit of paper. It is a 2-D figure.

The space the shape occupies on the article is called its Area. Consider your square as being composed of smaller unit squares.

So, we have the area of the rectangle as:

A(x)=2x^2+18x

Area formula: Area = length * width

So, the length of the rectangle will be:

Area = length * width

2x^2+18x = length * 2x

Length = (2x^2 + 18x) / 2x

With the help of long division:

2x√2x² + 18x

Length = x + 9

Therefore, using the area of the rectangle, we know that the length of the given rectangle is x + 9.

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Correct question:
The area of the rectangle is given by the polynomial function A(x)=2x^2+18x. If the width of the rectangle is 2x what is the length?

The correct decimal number for 17/22 will be equal to 0.7(727)bar.

The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. Decimal notation is the method of representing numbers in the decimal system. Decimal refers to the base-10 number system, which is perhaps the most widely used number system. The term "decimal number" refers to a number that has a decimal point followed by digits with values less than one.

Here,

17/22=0.772727.....

For 17/22, the proper decimal number is 0.7(727)bar.

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