Diego and Stacy can paint a doghouse in 5 hours when working together. Diego works twice as fast as Stacy. Let x be the number of hours it would take Diego to paint the doghouse and y be the number
of hours it would take Stacy to paint the doghouse. How long would it take Stacy
to paint the doghouse if she was working alone? How long would it take Diego to paint the doghouse if he was working alone?


Please show steps!

Answer: NM = 40

Step-by-step explanation:

    First, we will label everything. See attached.

    Next, we will set up a proportion to solve. Let the missing side, ? in the picture, be equal to x.

➜ On the left side will be the "smaller top" triangle

➜ On the right side will be the larger triangle

➜ View the second attachment for a visual explanation of this if you are confused.

[tex]\displaystyle \frac{x}{30}=\frac{x+24}{48}[/tex]

    Next, we will cross-multiply and solve.

[tex]\displaystyle \frac{x}{30}=\frac{x+24}{48}[/tex]

48x = 30(x + 24)

48x = 30x + 720

18x = 720

x = 40

Answer:

9

Step-by-step explanation:

Vertical angles are congruent, so:

[tex]16y=18y-18 \\ \\ -2y=-18 \\ \\ y=9[/tex]

Answer:

y = 9

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Therefore, equate the expressions and solve for y:

[tex]\begin{aligned}(18y-18)^{\circ}&=16y^{\circ}\\18y-18&=16y\\18y-18+18&=16y+18\\18y&=16y+18\\18y-16y&=16y+18-16y\\2y&=18\\2y \div 2 &=18 \div 2 \\y&=9\end{aligned}[/tex]

Therefore, the value of y is 9.

The values of the expression h(1), h(-7) and h(9) are 6, 50 and 62

After dividing one number by another, the modulo operation yields the remainder or signed remainder of the division.

Given the following modulus function shown below;

h(x)= |1 - 7x|, we are to find the following.

h(1)

h(-7)

h(9)

If x = 1, then;

h(x)= |1 - 7(1)|

h(1) = |1-7|

h(1) = |-6|

h(1) = 6

If x = -7, then;

h(-7)= |1 - 7(-7)|

h(-7) = |1--49)|

h(-7) = |1+49|

h(-7) = |50|

h(-7) = 50

If x = 9, then;

h(x)= |1 - 7(7)|

h(1) = |1-63|

h(1) = |-62|

h(1) = 62

This gives the equivalent values of the expression

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Usual selling price of a pair of shoes is $68 with discount 40% and sales tax 6% then total price of shoes including tax is equal to $43.248.

As given in the question,

Given that:

Usual selling price of shoes = $68

Discount on shoes =40%

Discounts an amount or percentage from something that they are selling, they take the amount or percentage off the usual price.

so, remove 40% from the price and you have left 60%

reduced price = 60% of $68

                         =60/100 * 68 = $40.8

Sales tax is 6% of reduced price= 6% of $40.8

                                           =$2.448 upto 3 decimal digits

Now , price including tax =$40.8+$2.448 =$43.248

Hence, total price including tax= $43.248

Therefore, usual selling price of a pair of shoes is $68 with discount 40% and sales tax 6% then total price of shoes including tax is equal to $43.248.

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Answer:

25

sum of the interior angles of triangle =180

101+54=155

155-180=25

The figure RSTU can represent Quadrilateral, Parallelogram and Rectangle

The figure KLMN  represents Quadrilateral and Parallelogram

The figure ABCD  represents only Quadrilateral

Given,

The figures;

RSTU, KLMN and ABCD

We have to identify the true facts about the figure.

All figure are drawn like a rectangle.

Quadrilateral;

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

Parallelogram;

A quadrilateral is referred to as a parallelogram in geometry. The opposite sides of a parallelogram are parallel and of equal length. Rhombus, rectangle, and square are a few instances of parallelograms.

Now here,

RSTU; This figure can represent all the options.

That is,

Quadrilateral, Parallelogram and Rectangle

KLMN; This figure represents Quadrilateral and Parallelogram

ABCD; This figure represents only Quadrilateral

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x = 9

x + 3 + x - 1 = 20

2x + 2 = 20

2x = 18

x = 9

The domain and range of the function f(x) = |x-1| +3 are-

For the given expression for the function;

f(x) = |x-1| +3.

Domain: Unless the expression is undefined, the domain of the representation is all real numbers. Because there is no real number in this case, the expression is undefined.

Interval Notation:(−∞,∞)

Set-Builder Notation:{x| x ∈ R}

Range: The range is indeed the collection of all possible y values. To determine the range, consult the graph.

Interval Notation:[3,∞)

Set-Builder Notation:{y| y ≥ 3}

Thus, the domain and the range of the function is estimated.

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Based on the equation of the line that is parallel to the first line, the equation of the line in slope-intercept form is y = 3/4x - 6³/₄

First, find the slope of 3x + 4y = 7:
( 3x + 4y = 7) x 1/4

3/4x + y = 7/4

The slope is therefore 3/4x.

Lines that are parallel to each other have the same slope. You can therefore use this slope to find the formula of the other line by first solving for the y-intercept:
y = Slope(x) + y-intercept

-9 = 3/4(-3) + y-intercept

y-intercept = -6³/₄

The equation of the line is:

y = 3/4x - 6³/₄

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If f(x) = 1/x, then the function representing the graph plotted will be -

y = f(x + 2) - 1.

The function f(x) = 1/x is called the multiplicative inverse function, because for each input it returns the multiplicative inverse or reciprocal of that input.

Given is function f(x) = 1/x.

The graph of the function f(x) = 1/x is plotted in the graph. If we plot the graph for f(x + 2) = 1/(x + 2), than the graph will shift towards left. If we subtract 1 from the f(x + 2), than the graph will shift downwards.

Therefore, if f(x) = 1/x, then the function representing the graph plotted will be -

y = f(x + 2) - 1

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The volume of the remaining solid correct to 2 decimal places is 3634.60 m³

From the question, we are to determine the volume of the remaining solid

Volume of the remaining solid = Volume of the larger prism - Volume of the rectangular prisms carved out

First, we will determine the volume of the larger prism

Volume of the larger prism = 17 × 17 × 17

Volume of the larger prism = 4913 m³

Now, we will determine the volume of one of the rectangular prism that was carved out

Volume = 4 × 9.4 × 17

Volume = 639.2 m³

∴ Volume of the two identical holes carved out = 2 × 639.2 m³

= 1278.4 m³

Thus,

Volume of the remaining solid = 4913 m³ - 1278.4 m³

Volume of the remaining solid = 3634.60 m³

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In case whereby Soledad says 3 (2-2)-1=36 the error she made was that ​she does not perform, the calculation base  PEDMAS  rule of mathematics.

The mathematical error can be described as the error that can be made when making a calculation, and the expected rule in mathematics in solving the particular problem is not followed.

From the given mathematical expression, 3 (2-2)-1=36, if we are to solve it, we will need to open the parenthesis first which will give us 6-6-1=-1, therefore it can be concluded that she make the mistake by not following the rules required.

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The value of (x + 5) * (x^3 + 6x^2 + 18x) is x^4 + 11x^3  + 48x^2 + 90x

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

How to evaluate the polynomial expression?

The polynomial expression is given as

(x + 5) * (x^3 + 6x^2 + 18x)

Express the polynomial expression as a product of factors

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x * (x^3 + 6x^2 + 18x) + 5 * (x^3 + 6x^2 + 18x)

Open the brackets in the polynomial expression

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 6x^3 + 18x^2 + 5x^3 + 30x^2 + 90x

Collect the like terms in the polynomial expression

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 6x^3 + 5x^3  + 18x^2 + 30x^2 + 90x

Evaluate the like terms in the polynomial expression

So, we have the following equation

(x + 5) * (x^3 + 6x^2 + 18x) = x^4 + 11x^3  + 48x^2 + 90x

Hence, the solution is x^4 + 11x^3  + 48x^2 + 90x

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Answer:

shifted 5 up and 4 to the left

Step-by-step explanation:

Answer:

<DKF IS 54° BECAUSE IT IS VERTICALLY OPPOSITE ANGLE OF THE<IKL.

Answer:

8.0/0.8

=10times

The value of x that makes the equation shown in the model true is x = -3.

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

The model shown can be represented by the equation:

4(-x) + 9(1) = 8(-x) + 3(-1)

-4x + 9 = -8x - 3

-4x + 8x = -3 - 9

4x = -12

x = -3

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Answer:

x = - 4, y = 2

Step-by-step explanation:

First equation: 4x + 3y = - 10

Second equation: 4x+y= - 14

To solve simultaneously:

Rearrange one of the equations and substitute the equation to another equation, I prefer rearranging the second equation because it is easier.

Rearranging the second equation to get y, and then substitute back to the first equation to find x:

y = - 14 - 4x ------> new second equation

Substitute y (new second equation) into the first equation to find x:

4x +3(-14 -4x) = - 10

4x - 42 - 12 x = - 10

       - 8x - 42 = -10

                -8x = - 10 + 42

               - 8x = 32

                 8x = - 32

                   x = - 4

Now we substitute x = - 4 to the second equation to find y:

4x + y = - 14

y = - 14 - 4(-4)

y = - 14 - (-16)

y = - 14 + 16

y = 2

£1 = 99.72 rupees -> £450 = 44874 rupees.

As the post office only has 500 rupee papers, once we calculate out the result, we have to round down to the nearest whole number.

The amount of rupee papers we can change out is : 44874 : 500 = 89.748 (papers)
We round down to 89 papers.

Answer:

x<-5.5   or x<-11/2

Step-by-step explanation:

2(4x+1)<3(2x-3)

1. First we need to expand the brackets

8x+2<6x-9

2. get the x on one side so we would -6x and -2 on each side

2x<-11

3. divide by 2 on each side as we want to get the value of x which gives

x<-11/2

the fraction can also be written as a decimal

x<-5.5

4) so, the final answer is

x<-5.5 or <-11/2

From the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.

As given in the question,

From the given figure:

line l is parallel to line m.

t is the transversal of line l and m

Relationship between angles for the parallel lines

∠1 and ∠2  are straight angles and are supplementary

∠3 and ∠2 are interior angles and are supplementary

⇒m(∠1 + ∠2) = m(∠3+∠2)

⇒m∠1= m∠3

Therefore, from the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.

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Q is the set of the rational numbers

Rational numbers are all numbers that can be put in the form of a/, where b is not equal to zero.

Examples:

The given equation is

Insert log on both sides

Use the rule of power with a log

Divide both sides by log(1/5)

Since we can not put the value of x in the form of a/b, then

The equation has NO solution in Q (or empty set { } or Nul)

4 1/6 divided by 8/9 is 4 11/16

The first step is to change the mixed fraction (4 1/6) to a proper fraction

4 1/6

= 4 × 6

= 24 + 1

= 25

= 25/6

The Fraction can be divided as follows

25/6 ÷ 8/9

= 25/6 × 9/8

= 75/16

= 4 11/16

Hence the result of the division of 4 1/6 and 8/9 is 4 11/16

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Answer:

Step-by-step explanation:

Fuel cost = (Distance / Consumption) × Cost per gallon.

107 X  4.83 = 516.81

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Answer:

-7

Step-by-step explanation:

Answer:

Step-by-step explanation:

-4 + (-3) is basically -4 - 3

-4 - 3 = -7

Answer:

Is 23

Step-by-step explanation:

His name 721 6 the y 8th 7th in his 6th grade 6th class and I was

The value of the x for the given expression [tex](32)^{1/25}\times (2)^x = (8)^{1/4}[/tex] is 19/20.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is

[tex](32)^{1/25}\times (2)^x = (8)^{1/4}[/tex]

Simplify the expression,

[tex]((2)^5)^{1/25}\times (2)^x = (2^3)^{1/4}\\\\(2)^{5/25}\times(2)^x =(2)^{3/4}\\\\(2)^{1/5}\times(2)^x = (2)^{3/4}\\(2)^{1/5 + x} = (2)^{3/4}\\[/tex]

The base is same, so the expression can be written as,

1/5 + x = 3/4

x - 3/4 = 1/5

x = 1/5 + 3/4

x = (4 + 15)/20

x = 19 / 20

The required value of x is 19/20.

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If the Employee: Curtis R. Evan with SSN: 5 5 5-55-5 5 55 has regular earning of $421 and overtime of $78. Curtis's net pay is $499.

Net pay can be defined as the amount a person received or earn as a salary after all deduction has been substracted.

Using this formula to determine the net pay

Net pay = Regular earnings + Overtime

Where :

Regular earning  = $421

Overtime = $78

Let plug in the formula

Net pay = $421 + $78

Net pay = $499

Therefore we can conclude that the net pay or take home amount is the amount of $499.

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The symbol that creates a true sentence for the expression is (16 - 8) ÷ 2 < 16 – 8 ÷ 2.

It should be noted that an expression is used to show the relationship between the values or the data given. This will be illustrated as thus:

It should be noted that (16 - 8) ÷ 2 will be:

(16 - 8) ÷ 2

= 2 ÷ 2

= 1

On the other hand, 16 - 8 ÷ 2 will be;

= 16 - 8 ÷ 2

= 16 - 4

= 12

It should be noted that 1 is less than 12. The symbol will be less than.

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The original dimensions are 12 m and 20 m.

What is area of rectangle?

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle.

Let x be the width of the rectangle.

Length of the rectangle = x+8

Area of the rectangle = x(x+8)

According to question, new width= x+2

New length = x+2+8 = x+10

New area = (x+2)(x+10)

Area increased = (x+2)(x+10) – x(x+8)

x^2+12x+20-x^2-8x=68

4x-20=68

4x=48

x=12

Hence, the width = 12m and length = 12+8 = 20 m

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