Find the difference 32 1/6 - 19 5/9

Answer:

30pqr

Step-by-step explanation:

\( \rm \: 2p \times 3q \times 5r = 2 \times 3 \times 5 \times p \times q \times r\)

Multiplying 2, 3, and 5 gives 30, so we have:

\( \rm \: 2p \times 3q \times 5r = 30 \times p \times q \times r\)

Therefore, the simplest form of 2p x 3q x 5r is 30pqr

Given

225 is 25 % of a number

Answer

let number be x

Answer: One way to calculate the percent increase in Robin's monthly bill is to use the following formula:

% increase = (new amount - original amount) / original amount x 100

In this case, the original amount is $120 and the new amount is $150. So, the calculation would be:

% increase = (150 - 120) / 120 x 100 = 30 / 120 x 100 = 0.25 x 100 = 25

Therefore, the percent increase in Robin's monthly bill is 25%.

Another way to calculate the percent increase is to use the formula:

(New amount - original amount) / original amount

In this case: (150-120)/120 = 0.25, and multiply by 100 to get 25%

So, both formula gives the same answer 25%

Step-by-step explanation:

Given:

The triangle ABC is reflected over the x-axis.

The distance between point A and A’ is 14.

To find:

The distance between the x-axis and A’.

Solution:

If a figure is reflected across the x-axis then the corresponding parts are mirror image of each other about the x-axis.

It means the distance between A and x-axis is same as the distance between x-axis and A'.

The distance between point A and A’ is 14.

Let d be the distance between the x-axis and A’. Then,

\(d+d=14\)

\(2d=14\)

\(d=\dfrac{14}{2}\)

\(d=7\)

Therefore, the correct option is 1.

\(\cfrac{2y}{3}-\cfrac{3}{4}=\cfrac{1}{12}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{2y}{3}-\cfrac{3}{4} \right)=12\left( \cfrac{1}{12} \right)}\implies 8y-9=1 \\\\\\ 8y=10\implies y=\cfrac{10}{8}\implies y=\cfrac{5}{4}\)

Answer:

0

Step-by-step explanation:

x < 4 means all numbers less than 4, excluding 4 itself.

4.5 > 4.

5 > 4.

so 0 is the solution

Answer:

4

Step-by-step explanation:

interval notation ( negative infinity, 4)

Answer:

t - 4 ≤ 4

Step-by-step explanation:

Hi I really need help with this

The number line represents t ≤ 8

Since the line is on 8 and moving towards the negative part of the number like (less than)

The equivalent equation will be;

t - 4 ≤ 4

Ads 4 to both sides

t-4+4≤4+4

t ≤ 8

Since the solution is similar to the expression above hence t - 4 ≤ 4 is correct

Answer:

\(m = 1\) -- Slope

\(y = x + 3\) --- Equation

Step-by-step explanation:

Given

\((x_1,y_1) = (0,3)\)

\((x_2,y_2) = (-4,-1)\)

Required

The slope and the equation

The slope (m) is calculated using:

\(m=\frac{y_2 - y_1}{x_2 - x_1}\)

\(m=\frac{-1-3}{-4- 0}\)

\(m=\frac{-4}{-4}\)

\(m = 1\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = 1(x - 0) + 3\)

\(y = 1(x) + 3\)

\(y = x + 3\)

Answer:

-5v + 6.2w - 3

Step-by-step explanation:

- (5v - 6.2w) -3

= -5v + 6.2w - 3

Answer:

the volume of the square pyramid is 2430 cubic cm

Answer:

1296 cm³

Step-by-step explanation:

V = a² x [√s²- (a/2)²] / 3

a = 18 cm

s = 15 cm

V = 18² x [√15²-(18/2)²] / 3 = 18² x [√225-81] / 3

V = 324 x (√144/3) = 1296 cm³

Answer:

(5, 4)

Step-by-step explanation:

(x + 2, y + 3)

(3  + 2, 1 + 3)

(5, 4)

Answer:

B' (5, 4 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 2, y + 3 )

means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then

B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

Answer:

\(D_{O,2} (x,y) = (2x, 2y)\)

Side Q'S' lies on a line with a slope of -1.

The distance from Q' to the origin is twice the distance from Q to the origin.

Step-by-step explanation:

The explanations are as follows

As we can see from the attached figure that the ΔQ'R'S' is dilated i.e transformation is made or change in size

Now

Based on

(x,y) = (2x,2y)

The intercepts are as follows

For S

(-1,1)  = (-2,2)

For Q

(-3,3) = (-6,6)

For S

(2,4) = (4,8)

Based on this we can say that the three above options are correct

Answer:

A, B, E on edge

Step-by-step explanation:

took the test :)

Answer:

True

Step-by-step explanation:

It passes the vertical line test, meaning you can draw a vertical line anywhere on the graph and it will only intersect at one point

this means that for every input (x value) there is only one output (y value)

Yes, The graph represents a function.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to show a graph.

Now, We know that;

The vertical line test, meaning you can draw a vertical line anywhere on the graph and it will only intersect at one point, then  it represent a function.

Here, The graph satisfy vertical line test, this means that for every input (x value) there is only one output (y value).

Thus, The graph represents a function.

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Answer:

the answer/expression you require is 40 - 1 = 1 day x - 1 = day 2 (repeat day 2 forever

Step-by-step explanation:

i say this because - 40 for the air conditioner and if it’s - 1 for electricity a day then unless your buying an air conditioner every day i don’t think you,l be repeating day 1 every day

:D

Answer:

y=3x+5

0 hours is $5

1 hour is $8

2 hours is $11

3 hours is $14

Step-by-step explanation:

y=mx+b

m = slope and b = y intercept

in this case 3 dollars an hour (x) would be m

and 5 rental fee would be B

Answer:

Graph C is the answer.

Step-by-step explanation:

Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.

Total expenditure is less than $3.

If we represent expense in the equation form then it will be

Expense on pencils + expense on erasers = Total expense which is < 3

0.25X + 0.50Y < 3

Now we divide the inequality by 0.25

X + 2Y < 12

This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.

Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)

Now we come to the graphs. Here dotted line graphs are A or C.

We will calculate the slopes of the lines from the graphs A and C to get tha answer.

For Graph A

The end points are (12, 0) and (0, 3)

So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4

For Graph C.

End points the line are (0, 6) and (12, 0)

Slope of the line = (0-6)/(12-0) = -6/12 = -1/2

Therefore Graph C is the answer.

Answer:

Graph C is the answer.

Step-by-step explanation:

Lola bought X pencils that cost $0.25 and Y erasers that cost $0.50.

Total expenditure is less than $3.

If we represent expense in the equation form then it will be

Expense on pencils + expense on erasers = Total expense which is < 3

0.25X + 0.50Y < 3

Now we divide the inequality by 0.25

X + 2Y < 12

This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.

Slope of this line is = (-1/2) {from the standard equation of line y = mx + c)

Now we come to the graphs. Here dotted line graphs are A or C.

We will calculate the slopes of the lines from the graphs A and C to get tha answer.

For Graph A

The end points are (12, 0) and (0, 3)

So slope = (y-y')/(x-x') = (3-0)/(0-12) = -3/12 = -1/4

For Graph C.

End points the line are (0, 6) and (12, 0)

Slope of the line = (0-6)/(12-0) = -6/12 = -1/2

Therefore Graph C is the answer.

Step-by-step explanation:

make brainiest please

The equation that represents the amount in dollars that she must pay for using the parking lot that month is y = 2x +10, the correct option is B.

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in determination of unknown parameters.

The equations are of various types, such as Trigonometric equations, quadratic equations.

The amount Tanesha pays to use the parking lot is $10

The daily amount she pays to use the parking is $2

Let x represents the days in one month.

Let y represents the amount in dollars that she must pay for using the parking lot that month.

The unknown parameters are x and y

The equation that can be formed is

y = 2x +10

It seems that your question is incomplete, the complete question is as follows:

A .  y = 2x

B. y = 2x +10

C. y = 10x +2

D. y = 10x

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Answer:

to solve the equation you first need to bring it to factors and by doing that you first need to let the equation equal 0 hence you need to minus 2 on both sides of the equation therefore

x^2 + 10x + 25 - 2 =2 - 2

therefore

x^2 + 10x +23 = 0

now since the equation cannot be factored, we use the formula.

x= \(\frac{-b +- \sqrt{b^{2}-4ac } }{2a}\)

where

a=1

b=10

c=23

note we use the coefficients only.

therefore x = \(\frac{-10 -+ \sqrt{10^{2}-4(1)(23) } }{2(1)}\)

=\(\frac{-10-+\sqrt{100-92} }{2}\)

=\(\frac{-10-+\sqrt{8} }{2}\)

then we form two equations according to negative and positive symbols

x=\(\frac{-10+\sqrt{8} }{2} or x =\frac{-10-\sqrt{8} }{2}\)

therefore x = \(-5+\sqrt{2}\)   or x=\(-5-\sqrt{2}\)

Hello!

\(\large\boxed{(4, -150)}\)

We can solve for the vertex by completing the square. Begin by factoring out 6 from the equation to simplify the process:

6(x² - 8x) - 54 = 0

To complete the square, we must look at the first two terms (x² - 8x).

Remember that squaring a binomial uses the format a² + 2ab + b². We are already given a² and 2ab², so solve for b:

-8 / 2 = -4. This is the value of b.

We can rewrite this as:

(x - 4)²

However, this produces +16 which much be taken into account. Substitute (x - 4)² into the original equation:

6(x - 4)² - 54 = 0

Multiply 16 by the term in the front and subtract to cancel out this term:

6(x - 4)² - 54 - (6 · 16) = 0

Simplify:

6(x - 4)² - 150 = 0

In this form, the vertex is given as:

a(x - h)² + k, where h = x-coordinate and k = y-coordinate of the vertex.

In this instance, h = 4 and k = -150, so the coordinates of the vertex are:

(4, -150)

Answer:

y = 6x²-48x-54 has a vertex at (4,-150)

Step-by-step explanation:

There is no vertex. The solution set to 6x²-48x-54 = 0 is two points, (-1,0) and (9,0).

If you mean y = 6x²-48x-54, that is an up-opening parabola.

Put the equation into vertex form:

y = 6x²-48x-54

 = 6(x²-8x)-54

 = 6(x²-8x+4²)-6·4²-54

 = 6(x-4)² - 150

vertex at (4,-150)

Answer:

54

Step-by-step explanation:

90-36=54

The exponential expression can be written as \(y = 25.70(1.15)^x\).

The exponential functions are those with the formula f(x) = a. x. In this case, a ( 0) is known as the base, and x is known as the exponent. Explanation: Exponential functions are those with the formula \(a^x\).

Given that Data set (2, 34) (4,45) (6,51) (8,68) (10,71) (12,79) (14,88). The exponential expression can be written as:-

\(y = ab^x\)

At points (2, 34) and (4,45). Solve the equations and find the value of a and b.

34 = ab²

45 = ab⁴

b⁴ / b² = 45 / 34

b² = 1.32

b = √1.32

b = 1.15

The value of a will be:-

34 = ab²

34 = a x (1.15)²

a = 25.70

The exponential equation can be written as:-

\(y = ab^x\)

\(y = 25.70(1.15)^x\)

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Answer:

area = 4

Step-by-step explanation:

area = length × width

length= 3 1/3 =3/3 = 1 and width= 3

area = 1 × 3

= 4

Answer:

(sec θ - tan θ)²

= sec² θ –2 sec θ tan θ + tan² θ

The function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4 is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

A function is said to be continuous if there are no breaks or jumps in the functions

Conditions for continuity of a function

Now, for the given function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4

We need to determine the interval of continuity, We proceed as follows.

Since f(x) = sin⁻¹x, x ≠ π/4 , we know that the minimum value of x is - 1 and its maximum value is 1.

So, x must lie in the interval (-1, 1) for x ≠ π/4,

Now, when x = π/4 f(x) = sinx. We know that x = π/4 lies in the interval (-1, 1).

But we know that f(x) = sinx at x = π/4. So, there is a removable discontinuity at x = π/4.

So, from the left, f(x) is continuous on the interval [-1, π/4) and  from the right, f(x) is continuous on the interval (π/4, 1]

So, combining both intervals, we have f(x) is continous on the interval [-1, π/4) ∪ (π/4, 1] and since f(x) = sinx at x = π/4, there is a removable discontinuity at x = π/4

So, the function f(x) is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

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Since each term can be written as the previous term divided by three, this is a geometric sequence.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

For this problem, we have that each term can be written as the previous term multiplied by one third or divided by three, hence the division of consecutive terms is always the same and this is a geometric sequence.

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