A business owner spent $4000 for a computer and software. For bookkeeping purposes, he needs to post the price of the computer and software separately. The computer costs 4 times as much as the software. What is the cost of the computer?

The formula of a volume of a cuboid:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have:

l = (x + 4) cm

w = (x + 1) cm

h = 3 cm

Substitute:

[tex]V=(x+4)(x+1)(3)[/tex]      use distributive property

[tex]V=(x+4)(3x+3)[/tex]

[tex]V=(x)(3x)+(x)(3)+(4)(3x)+(4)(3)[/tex]

[tex]V=3x^2+3x+12x+12[/tex]      combine like terms

[tex]\boxed{V=3x^2+15x+12}[/tex]

The reflexive property justifies the statement "If CD = EF, then CD = EF".

The reason that justifies the statement "If CD = EF, then CD = EF" is the reflexive property.

The reflexive property states that any geometric shape or object is always equal to itself. In this case, CD is equal to itself, and EF is equal to itself, so if CD = EF, then CD will always be equal to EF.

Therefore, option B, the reflexive property, is the correct reason for the given statement.

Learn more about Reflexive property

https://brainly.in/question/27640923

#SPJ3

Answer:

Parallel bases.

   The legs are congruent by definition.

   The lower base angles are congruent.

   The upper base angles are congruent.

   Any lower base angle is supplementary to any upper base angle.

   The diagonals are congruent.

Step-by-step explanation:

Answer:

480

Step-by-step explanation:

Divide 100 by 37.5

Multiply 180 by that number

100/37.5=2.667'

180*2.667=480

Anne surveyed 480 people.

Answer:

y = -3x - 7

Step-by-step explanation:

Slope = (8 - 2)/(-5 + 3) = 6/-2 = -3

Equation

y - 2 = - 3(x + 3)

y - 2 = -3x - 9

y = -3x - 7

Answer

y=-3x-7

is the equation of line that passes through the points (-3,2) and (-5,8)

step by step explanation:

we are given

(x1,y1)=(-3,2)

(x2,y2)=(-5,8)

formula of slope

m=(y2-y1 )/ (x2-x1)

putting value in formula

m=(8-2) /-5-(-3)

m=6/-5+3

m=6/-2

m=-3

Formula of line slop form of equation is

y-y1=m(x-x1)

putting the values in the formula

y-2= -3(x-(-3))

y-2= -3(x+3)

y-2=-3x-9

y=-3x-9+2

y=-3x-7

is the equation of line that passes through the points (-3,2) and (-5,8)

When raising a monomial to a power, you multiply the exponents of each variable by that power.

When you raise a monomial to the power of 2, you multiply the exponents of each variable by 2. So in the given monomial ax6y12, you would raise each exponent to the power of 2 to get a2x12y24.

Similarly, when you raise a monomial to the power of 3, you multiply the exponents of each variable by 3. So in the given monomial ax6y12, you would raise each exponent to the power of 3 to get a3x18y36.

https://brainly.com/question/9183135

#SPJ3

Answer:

6 a^3 b^8

Hope That Helps!

The value of x is the point of intersection of the graphs of [tex]\mathbf{P =12 + 2x}[/tex] and [tex]\mathbf{A =6x}[/tex]

The value of x is 3

The given parameters are:

[tex]\mathbf{Length = 6}[/tex]

[tex]\mathbf{Width = x}[/tex]

The perimeter is calculated as:

[tex]\mathbf{P =2 \times (Length + Width)}[/tex]

So, we have:

[tex]\mathbf{P =2 \times (6 + x)}[/tex]

Expand

[tex]\mathbf{P =12 + 2x}[/tex]

The area is calculated as:

[tex]\mathbf{P = Length \times Width}[/tex]

So, we have:

[tex]\mathbf{A =6 \times x}[/tex]

[tex]\mathbf{A =6x}[/tex]

See attachment for the graphs of [tex]\mathbf{P =12 + 2x}[/tex] and [tex]\mathbf{A =6x}[/tex]

From the attached graph, the lines of both functions meet at x =3.

Hence, the value of x is 3

Read more about linear equations at:

https://brainly.com/question/11897796

Answer:

It will take them 18 hours.

Step-by-step explanation:

To find the answer of this, you must first multiply the amount of people by the time:

6 * 15 = 90

Then to find the time it takes 5 workers, divide this by 5:

90 ÷ 5 = 18

So it will take them 18 hours!

Answer:

It solves all quadratic equations for any real or imaginary solutions.

Step-by-step explanation:

The quadratic formula is

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].

It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions.

Answer:

5/6

Step-by-step explanation:

1/2 / 3/5

1/2*5/3

5/6

Answer:

5/6

Step-by-step explanation:

1/2 ÷ 3/5

Copy dot flip

1/2 * 5/3

5/6

Answer:

[tex]y=\frac{3}{2} x+6[/tex]

Step-by-step explanation:

We are given the following equation and we are supposed to solve y in terms of x. It simpler terms, it means that we have to make y the subject of the equation while x being used in it as it is:

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

Taking the constant 4 to the side where x is to get:

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

Multiplying the denominator 3 to the other side of the equation to get:

[tex]2y=3x+12[/tex]

Isolating y to make it the subject:

[tex]y=\frac{3}{2} x+\frac{12}{2}\\ \\y=\frac{3}{2} x+6[/tex]

Answer:

The Jar contained 5^67 pennis of nickels and quaters. Making a lot of money in 1/4 of a month. The 5he value of the pennies in the bigger than the amount of the total fitting of itself. The Largest pennies in the jar depended on the nickels and quaers inside. The 133 pennies wer the jar that contained the lesser amount of pennies, therfore the bigger jar standes with a larger value

Step-by-step explanation:

Answer:

The square has 4-fold reflectional symmetry. The regular octagon has 8-fold symmetry.

Step-by-step explanation:

For a square,

There are two lines of symmetry along two diagonals and

two lines of symmetry along midpoints of two pairs of opposite sides.

Therefore, there are 4 lines of reflectional symmetry in total.

For a regular octagon,

There are four lines of symmetry along four diagonals and

four lines of symmetry along midpoints of four pairs of opposite sides.

Therefore, there are 8 lines of reflectional symmetry in total.

Final answer:

A square has 4-fold reflectional symmetry, while a regular octagon has 8-fold reflectional symmetry.

Explanation:

Reflectional symmetry refers to a property of a shape where it can be divided into two mirror-image halves. The -fold reflectional symmetry of a regular polygon refers to the number of lines of symmetry it possesses. A line of symmetry is an imaginary line that divides the shape into two equal halves that are mirror images of each other.

For example, a square has 4-fold reflectional symmetry because it has 4 lines of symmetry, dividing it into 4 equal halves. Each line of symmetry passes through the midpoints of opposite sides.

On the other hand, a regular octagon has 8-fold reflectional symmetry because it has 8 lines of symmetry, dividing it into 8 equal halves. Each line of symmetry passes through the midpoints of opposite sides or vertices.

Answer:

According to the question,

Numbers are : 23 and -6

The two numbers are -6 and 23.

To find the two numbers, we can set up a system of equations based on the given information. Let the two numbers be [tex]\( x \) and \( y \), where \( x > y \)[/tex]. According to the problem, we have:

1. The sum of the two numbers is 17:

[tex]\[ x + y = 17 \][/tex]

2. The difference between the two numbers is 29:

[tex]\[ x - y = 29 \][/tex]

Now, we can solve this system of equations. We can add the two equations together to eliminate [tex]\( y \)[/tex] :

[tex]\[ (x + y) + (x - y) = 17 + 29 \] \[ 2x = 46 \] \[ x = \frac{46}{2} \] \[ x = 23 \][/tex]

Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into one of the original equations to find [tex]\( y \)[/tex]. Let's use the first equation:

[tex]\[ 23 + y = 17 \] \[ y = 17 - 23 \] \[ y = -6 \][/tex]

Therefore, the two numbers are 23 and -6.

Answer:

y = √7

Step-by-step explanation:

This circle has a center at (0,0) and a radius of 4 so its equation is:-

x^2 + y^2 = 16

when x= -3, (-3)^2 + y^2 = 16

9 + y^2 = 16

y^2 = 7

y = √7

Answer: [tex]\bold{k=\dfrac{1}{9}}[/tex]

Step-by-step explanation:

The constant of proportionality is y = kx.  Solve the given equation for "y" to find k-value in front of "x".

    18y = 2x

   [tex]\dfrac{18y}{18}=\dfrac{2x}{18}[/tex]

    [tex]y=\dfrac{1}{9}x[/tex]

[tex]k=\dfrac{1}{9}[/tex]

Simplify 7/5x to 7x/5

3(7x/5 + 4) -2(3/2 - 5/4x)

Simplify 5/4x to 5x/4

3(7x/5 + 4) -2(3/2 - 5x/4)

Expand

21x/5 + 12 - 3 + 5x/2

Collect like terms

(21x/5 + 5x/2) + (12 - 3)

Simplify

67x/10 + 9

The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x)  is (67x + 90)/10

Expression is a mathematical statement which consists of variables , constant and mathematical operators all together simultaneously.

The given expression is 3(7/5x+4)-2(3/2-5/4x)

[tex]\rm 3 ( \dfrac{7}{5} x+4) -2 ( \dfrac{3}{2}-\dfrac{5}{4}x)[/tex]

(21/5)x +12 - 3 + (5/2)x

((42+25)/10)x + 9

(67x + 90)/10

The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x)  is (67x + 90)/10

To know more about Expression

https://brainly.com/question/14083225

#SPJ2

19 x (42 + 58) or 19*(42 + 58) is the expression she can use. You factor out the common term 19. The distributive rule says that we can multiply the outer 19 with each term inside to get the original expression again.

After graphing both lines, we're able to tell the solution by looking at the point where the lines cross. In this case, it's at (4, -1). And so that is the solution set.

Answer: I know it’s a circle but I forget why actually sorry that doesn’t help much

Step-by-step explanation:

Answer:

363.6

Step-by-step explanation:

250/11= 22.72

22.72 x 16= 363.3636

when rounded tot he nearest tenth its 363.6 because the three is less than five and cannot bump up the 6

if possible make my answer the brainliest

Answer:

Find the negative reciprocal of the slope of the original line and use the slope-intercept form

y=mx+b to find the line perpendicular to [tex]y=2x+5[/tex].

[tex]y=−12x−5[/tex]

Hope this helps!!

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have}\ k:y=2x+5\to m_1=2.\\\\l:y=mx+b\to m=-\dfrac{1}{2}\to y=-\dfrac{1}{2}x+b.\\\\\text{The line passes through the point (-2, -4).}\ \text{Put the coordinates to the equation:}\\\\-4=-\dfrac{1}{2}(-2)+b\\\\-4=1+b\qquad\text{subtract 1 from both sides}\\\\-5=b\to b=-5\\\\Answer:\ \boxed{y=-\dfrac{1}{2}x-5}[/tex]

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

x + y = -3      subtract x from both sides

y = -x - 3

Answer:

80°

Step-by-step explanation:

Three angles are equal

Let the equal angle be x

3x+120=360

3x=240

x=240/3

=80

Hence the three angles are 80∘

Answer:

Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.

Step-by-step explanation:

The sum of the measures of the angles of an n-sided polygon is (n - 2)180.

A quadrilateral has 4 sides, so n = 4 in the formula above.

(n - 2)180 = (4 - 2)180 = 2(180) = 360

The sum of the measures of the angles of a quadrilateral is 360 degrees.

Three angles are congruent. Let the measures of the three congruent angles be x. The sum of the measures of the 3 angles is x + x + x = 3x.

The sum of the measures of the angles is 360 deg.

3x + 120 = 360

Subtract 120 from both sides.

3x = 240

Divide both sides by 3.

x = 80

Answer: Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.

Answer:

(a)

Given: A line passes through the points (3, -2) and (6, 2)

Point slope form: An equation of line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:

[tex]y -y_1=m(x-x_1`)[/tex]  .....[1] where m is the slope of the line.

Calculate first the slope of the line:

Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given points;

[tex]m = \frac{2-(-2)}{6-3}=\frac{2+2}{3} =\frac{4}{3}[/tex]

Substitute the value of m in [1] ;

[tex]y - (-2) = \frac{4}{3}(x-3)[/tex]

[tex]y+2=\frac{4}{3}(x-3)[/tex]     ......[1]

therefore, the equation of line in point slope form is, [tex]y+2=\frac{4}{3}(x-3)[/tex]    

(b)

to find the standard form of the equation [1]

Multiply both sides by 3  in [1] we get;

[tex]3(y+2) = 4(x-3)[/tex]

using distributive property;   [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]

3y + 6 = 4x -12

Subtract 3y to both sides we get;  

3y + 6 -3y = 4x - 12 - 3y

Simplify:

6 = 4x - 3y -12

Subtract 6 from both sides we get;

0 = 4x - 3y -12-6

Simplify:

4x - 3y - 18 =0

Therefore, the standard form of the equation is; 4x - 3y - 18 =0

Answer:

-8

Step-by-step explanation:

All you have to do to solve this equation is plug "-3" into the equation where you see "x"

[tex]f(x)=-x^2+1\\f(-3)=-(-3)^2+1\\f(-3)=-(9)+1\\f(-3)=-9+1\\f(-3)=-8[/tex]

Answer:

C. 105°

Step-by-step explanation:

To find the answer, we can use the method of exterior angle of triangles, which would be <A + <B = <C, in which A and B is any interior angles of triangles and C would be the exterior angle for the remaining angle.

In this case:

45°+60° = 105°

Therefore the answer is C. 105°

Hope it helps!

The measure of the angle x is 105 degrees option (C) is correct.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have a triangle shown in the picture.

As we know,

The sum of two interior angles is equal to the exterior angle;

The measure of the angle x:

x = 60 + 45

x = 105 degrees

Thus, the measure of the angle x is 105 degrees option (C) is correct.

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ2

a. 0.927

We have:

0.98 – 0.053

We can re-write it as:

0. 9 8 0 -

0. 0 5 3

Moving digits to the right:

0. 9 7 10 -

0. 0 5 3

Digit-per-digit subtraction:

0. 9 2 7

b. 0.27

We have:

0.67 – 0.4

We can re-write it as:

0. 6 7 -

0. 4 0

Digit-per-digit subtraction:

0. 2 7

c. 0.298

We have:

0.3 – 0.002

We can re-write it as:

0. 3 0 0 -

0. 0 0 2

Moving digits to the right:

0. 2 10 0 -

0. 0 0 2

Again:

0. 2 9 10 -

0. 0 0 2

Digit-per-digit subtraction:

0. 2 9 8

d. 2.411

We have:

3.2 – .789

We can re-write it as:

3. 2 0 0 -

0. 7 8 9

We need to rewrite the first term by moving digits to the right several times:

3. 2 0 0 = 2. 12 0 0 = 2. 11 10 0 = 2. 11 9 10

So now we have:

2. 11 9 10 -

0. 7 8 9

Digit-per-digit subtraction:

2. 4 1 1

e. 2.232

We have:

6.53 – 4.298

We can re-write it as:

6. 5 3 0 -

4. 2 9 8

We need to rewrite the first term by moving digits to the right several times:

6. 5 3 0 = 6. 5 2 10 = 6. 4 12 10

So now we have:

6. 4 12 10 -

4. 2 9 8

Digit-per-digit subtraction:

2. 2 3 2

f. 1.68

We have:

6 – 4.32

We can re-write it as:

6. 0 0 -

4. 3 2

We need to rewrite the first term by moving digits to the right several times:

6. 0 0 = 5. 10 0 = 5. 9 10

So now we have:

5. 9 10 -

4. 3 2

Digit-per-digit subtraction:

1. 6 8

g. 4.426

We have:

7 – 3.574

We can re-write it as:

7. 0 0 0 -

3. 5 7 4

We need to rewrite the first term by moving digits to the right several times:

7. 0 0 0 = 6. 10 0 0 = 6. 9 10 0 = 6. 9 9 10

So now we have:

6. 9 9 10 -

3. 5 7 4 =

Digit-per-digit subtraction:

3. 4 2 6

h. 3.03

We have:

4.83 – 1.8

We can re-write it as:

4. 8 3 -

1. 8 0

We can immediately do the digit-per-digit subtraction:

3. 0 3

i. 2.9

We have:

3.7 – 1.8

We can re-write it as:

3. 7 -

1. 8

We need to rewrite the first term by moving digits to the right:

3. 7 = 2. 17

So now we have:

2. 17 -

1. 8 =

Digit-per-digit subtraction:

2. 9

j. 4.538

We have:

16.17 – 11.632

We can re-write it as:

1 6 . 1 7 0 -

1 1 . 6 3 2

We need to rewrite the first term by moving digits to the right:

1 6. 1 7 0 = 1 6. 1 6 10 = 1 5. 11 6 10  

So now we have:

1 5. 11 6 10 -

1 1. 6 3 2 =

Digit-per-digit subtraction:

0 4. 5 3 8