Word Problem
(D) Joshua is going shopping for (E) paintings and (F) spoons. The cost of (E) painting is (B) 10$ and the cost of each (F) spoon is (A) 8$.
If (D) Joshua can spend at most (C) 100$, how many (F) spoons can be purchased?

3. Write an inequality of the form Ax + B ≤ C to represent the word problem using your answers for A, B, and C. Solve the inequality and show your work.


4. Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line.

The results of the expression 9 and 1/9 subtracted by 1 and 4/5 is 7 14/45

9 and 1/9 subtracted by 1 and 4/5

= 9 1/9 - 1 4/5

= 82/9 - 9/5

= (410-81) / 45

= 329/45

= 7 14/45

Therefore, 9 and 1/9 subtracted by 1 and 4/5 is 7 14/45

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Answer:

[tex]-2-i[/tex] I'm assuming there's a d option maybe? because this should be the answer

Step-by-step explanation:

Well you have the equation:

r-s

So all you need to do is plug in 1+2i as r, and 3+3i as s, and then you add like terms (kind of like how you can do 2 * sqrt(2) - 3 * sqrt(2) and you simply subtract the "coefficients")

[tex](1+2i)-(3+3i)[/tex]

Distribute the negative sign:

[tex]1+2i-3-3i[/tex]

Combine like terms

[tex](1-3)+(2i-3i)[/tex]

Simplify:

[tex]-2-i[/tex]

Answer:

Step-by-step explanation:

If 2u-6=4, let's solve for u.

Add 6 to both sides

2u-6+6 = 4+6

Simplify

2u = 10

Divide both sides by 2

u = 5

Now, we can solve u-5

5-5 = 0

The slope of the line will be – 1/5. Then the correct option is B.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

Take two point from the graph.

(0, 2) and (1, –3)

Then the slope will be

m = (2 – (–3)) / (0 – 1)

m = 5 / (–1)

m = – 1/5

Then the correct option is B.

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Answer:

-x + 7 / x + 1

Step-by-step explanation:

6 -(x - 1)/ x + 1

Apply distributive law: -(x - 1) = -x + 1

= 6 - x + 1 / x +1

Group like terms:

= -x + 7/ x + 1

Answer:  its 5x+7/x+1

Step-by-step explanation:

Observe the graph below. This graph represents the scenario.

The question is ill formated, the complete question is

In a simulation, a moving object accelerates from rest to 4 meters per second in 2 seconds. For the following three seconds, it increases linearly until it reaches a speed of 10 meters per second. Following three seconds at that speed (acceleration = 0), the item progressively decelerates until it comes to rest two seconds later. Draw the graph of this scenario for 10 seconds?

I'll describe how the graph may show.

It will move diagonally upward from time 0 to 2 seconds until it reaches the y axis at a speed of 4 m/s.

Then, from 2 to 5, the position will move up diagonally until it reaches the y axis at a speed of 10 m/s.

The next 5 to 8 seconds will be horizontal.

After that, it will descend diagonally.

Observe the graph below. This graph represents the scenario.

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Answer:

1/9m. just take 2/9- 1/9 then you'll get the material remaining good day.

Using the concept of subtraction of fractions, Jillian have 1/9m of cloth left.

Fractions are a way to represent numbers that are not whole numbers. They represent parts of a whole or divisions of a quantity. A fraction consists of two parts: a numerator and a denominator.

The numerator is the number on the top of the fraction and represents the number of parts being considered or counted. The denominator is the number on the bottom of the fraction and represents the total number of equal parts into which the whole is divided.

In this problem, we can easily determine the amount of cloth she have left.

Since she used 1/9 of it, we can proceed as;

2/9 - 1/9 = 1/9m

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Answer:

A

Step-by-step explanation:

27÷36=.75

.75= 3/4

decimal= fraction

Answer:

y = 4x + 11

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 = 4x - 2 ← is in slope- intercept form

with slope m = 4

• Parallel lines have equal slopes , then

y = 4x + c ← is the partial equation

to find c substitute (- 2, 3 ) into the partial equation

3 = - 8 + c ⇒ c = 3 + 8 = 11

y = 4x + 11 ← equation of line

Answer: D

Step-by-step explanation:

Answer: Choice D

Open hole at -3 with shading to the left.

==========================================================

Explanation:

The inequality [tex]-3 > \text{x}[/tex] is the same as [tex]\text{x} < -3[/tex]

When swapping both sides, the inequality sign flips as well.

Since we're looking for numbers smaller than -3, this includes things like -4, -5, -6, -7, and so on. Therefore we shade to the left of -3 on the number line.

We have an open hole at -3 to indicate it's not included as part of the solution set. We would include it if there as an "or equal to" as part of the inequality sign.

The equivalent expression of [tex]6^\frac 25[/tex] is [tex](\sqrt[5]{6})^2[/tex]

The expression is given as:

[tex]6^\frac 25[/tex]

The law of indices states that:

[tex]a^\frac mn = (\sqrt[n]{a})^m[/tex]

Using the above as a guide, we have:

[tex]6^\frac 25 = (\sqrt[5]{6})^2[/tex]

Hence, the equivalent expression of [tex]6^\frac 25[/tex] is [tex](\sqrt[5]{6})^2[/tex]

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Step-by-step explanation:

it is not clear - is 500 miles the whole round trip, or is it only the trip in one direction ?

and do we need the time for the whole round trip, or only for the return trip ?

in any case, always remember,

speed = distance/time

therefore, to get time, we need to divide distance by speed :

distance / distance/time = time×distance/distance = time

so, let's calculate all these different scenarios :

1. 500 miles is only one direction, and we measure only the time going back with 60 mph :

500 / 60 = 50/6 = 25/3 = 8 1/3 = 8 hours 20 minutes.

as 1/3 of 1 hour = 1/3 of 60 minutes = 60/3 = 20 minutes.

2. 500 miles is only one direction (going 1000 miles altogether), and we measure the time going to with 50 mph and going back with 60 mph :

500 / 50 = 10 hours

500 / 60 = 8 hours 20 minutes

the whole round trip takes 18 hours 20 minutes.

3. 500 miles is the whole round trip. so, 250 miles is one direction. and we measure only the time going back with 60 mph :

250 / 60 = 25/6 = 4 1/6 = 4 hours 10 minutes.

as 1/6 of 1 hour = 1/6 of 60 minutes = 60/6 = 10 minutes.

4. 500 miles is the whole round trip. so, 250 miles is one direction. and we measure the time going to with 50 mph and back with 60 mph :

250 / 50 = 5 hours

250 / 60 = 4 hours 10 minutes

the whole round trip takes 9 hours 10 minutes.

did you notice ?

when going only half the distance, also the time it takes to travel that distance is only half (or vice versa - double). because the ratio distance/time is always the same.

The formula for simple interest is the following:

[tex]S=Prt[/tex]

In this formula, [tex]S[/tex] is the amount of interest, [tex]P[/tex] is the principal (or initial) amount, [tex]r[/tex] is the interest rate, and [tex]t[/tex] is the length f time, typically in years.

First, let's make a couple of changes to how we wrote down the variables.

Substitute in the values and solve with a calculator.

[tex]\begin{aligned}S&=16,500\cdot0.06\cdot0.5\\&=\boxed{495}\end{aligned}[/tex]

3x + 6 = 48 (alternate angles are equal)

- 6

3x. = 42

÷3

x = 14 degrees

180-48 - 2y + 5y-9 =180

123 + 3y = 180

-123

3y = 57

÷3

y = 19 degrees

Explanation:

To find the last angle on the top straight line, do:

180 - (the 2 given angles).

So, 180 - (3x + 16, which is 48 due to alternate angles being equal). Then, minus the 2y.

(180 - 48 - 2y) & simplify => 132 - 2y

This gives you the equation for the missing angle on our top straight line.

Thus, co-interior angles add to 180. So, we add the new equation (132 - 2y) to 5y - 9.

Simplify

=> 123 + 3y (because - 2+5 =3)

and put it equal to 180. Solve for y

Hope this helps!

Answer:

y-2=2(x-5), y=2x-8, y+16=2(x+4)

Step-by-step explanation

Answer:

x = 41* & y = 90.

Step-by-step explanation:

Since we know that the figure is a right triangle, we can solve for y easily, as 90+y = 180

y = 90

to solve for x, we have 49+90+x, since the angle that makes up the left side is perpendicular to the triangle,

so 139+x = 180

x = 180-139

x = 41

Answer: A

Step-by-step explanation:

[tex]\frac{2}{3}x-5 < 11\\\\\frac{2}{3}x < 16\\ \\ x < 24[/tex]

The complement is 10%

The proportion is given as:

p = 90%

The complement is calculated as:

Complement = 100% - p

This gives

Complement = 100% - 90%

Evaluate the difference

Complement = 10%

Hence, the complement is 10%

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Answer:

[tex] {x}^{2} - 16 = 0 \: is \: the \: equation[/tex]

Step-by-step explanation:

[tex]x = - 4 \\ or \: x = 4[/tex]

[tex](x + 4) = 0 \: or \: (x - 4) = 0 \\ (x + 4)(x - 4) = 0 \\ open \: the \: bracket[/tex]

[tex]x(x - 4) + 4(x - 4) = 0[/tex]

[tex] {x}^{2} - 4x + 4x - 16 = 0 \\ {x}^{2} - 16 = 0[/tex]

The formula of P(x) = -0.7 (x-2)²(x+4)

A root of a polynomial is defined as the point or value at which the overall value of the polynomial = 0

It is given that

for a polynomial of degree 3

root x=2, multiplicity 2:  (x-2)²

root x= - 4, multiplicity 1:  (x+4)                  ³ ²

P(x) = a(x-2)²(x+4)

here a is constant

y-intercept =  -11.2

P(0) = -11.2

a(0-2)²(0+4) = -11.2

a * 4 * 4  = -11.2

16a = -11.2

a = -11.2/(16)

a= -11.2/16

P(x) = -(11.2/16)(x-2)²(x+4)

P(x) = -0.7 (x-2)²(x+4)

Therefore the formula of P(x) = -0.7 (x-2)²(x+4)

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Answer:

Step-by-step explanation:

convert to meters

6 dm = 0.6 m

40 mm = 0.04 m

2 m = 2 m

10 cm = 0.1 m

sum

0.6 + 0.04 + 2 + 0.1 =

2.74 m

Answer:

2.74m

Step-by-step explanation:

Convert all values to meters.

6dm = 0.6m

40mm = 0.04m

2m = 2m

10cm = 0.1m

sum = 0.6+0.04+2+0.1

= 2.74

Answer:

Center: (-4, 1)

Radius: √2

Explanation:

Circle general equation is represented by (x - h)² + (y - k)² = r²

where (h, k) is the center and "r" resembles radius

To write in general equation form, start completing square:

x² + y² + 8x -2y + 15 = 0

x² + 8x + y² - 2y + 15 = 0

(x + 4)² - 4² + (y - 1)² - (-1)² + 15 = 0

(x + 4)² + (y - 1)² - 16 - 1 + 15 = 0

(x + 4)² + (y - 1)² - 2 = 0

General equation form:

(x - (-4))² + (y - 1)² = (√2)²

From here, comparing with the formula equation.

It is determined: center: (-4, 1) and radius: √2

Answer:

center = (-4, 1)

radius = √2

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

Given equation:

[tex]x^2+y^2+8x-2y+15=0[/tex]

Subtract 15 from both sides to move the constant to the right side of the equation:

[tex]\implies x^2+y^2+8x-2y=-15[/tex]

Rearrange the left side to collect like variables:

[tex]\implies x^2+8x+y^2-2y=-15[/tex]

Add the square of half the coefficients of the variables x and y to both sides:

[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2+y^2-2y+\left(\dfrac{-2}{2}\right)^2=-15+\left(\dfrac{8}{2}\right)^2+\left(\dfrac{-2}{2}\right)^2[/tex]

[tex]\implies x^2+8x+16+y^2-2y+1=2[/tex]

Factor the two perfect square trinomials on the left side:

[tex]\implies (x+4)^2+(y-1)^2=2[/tex]

Compare the found equation with the general form to find the center and radius of the circle:

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Answer:

7/12 or 0.5833

Step-by-step explanation:

So you're going to have 36 combinations, because for each number 1-6 which may be rolled for the first roll, you're going to also have 6 other possible numbers for the second roll. This gives you 6 * 6 or 36. So you could define the entire sample space, but you could also just list the sample space with all the sums less than 7 that way you don't have to list all of the sample space, since you already know how many combinations there are going to be

Let's start with the case that you roll a 1, for the first roll:

1+1 = 2

1+2 = 3

1+3=4

1+4=5

1+5=6

These are the only combinations that will be less than 7 so stop here

Now do the case where you roll a 2, for the first roll

2+1 = 3

2+2= 4

2+3 = 5

2+4 = 6

The next roll will result in a roll greater than 6. This time there were only 4 combinations which is one less than the previous. This makes sense, since you're still increasing in intervals of 1, except the starting number is increasing by 1, meaning as the first roll increases, the amount of combinations with that starting roll that are below 7, will decrease by 1. So this means that:

1: 5 combinations

2: 4 combinations

3: 3 combinations

4: 2 combinations

5: 1 combination

6: 0 combination

This means there are going to be a total of 15 combinations which are less than 7, that means there are 36-15 combinations which are greater than or equal to 7. This simplifies to 21/36 which simplifies to 7/12. This can also be expressed as: 0.5833

Answer:

No ! The only thing that will take a wave or curl out of a synthetic wig is heat.

Step-by-step explanation:

Answer:

( x-7) ( x-5)

Step-by-step explanation:

x^2 -12x + 35

To factor this problem, we want to know that two numbers multiply to 35 and add to -12

-7 * -5 = 35

-7 + -5 = -12

( x-7) ( x-5)

Answer:

The answer is (x-7)( x-5)

Step-by-step explanation:

We need to find two numbers that add up to −12 and those same two numbers should have a product of 35

Here the common factors are -7 and -5 because when added they give -12 and when multiplied they give 35.

Therefore we write the answer as (x-7)(x-5)

Answer:

3/500

Step-by-step explanation:

.6%   = .006   =    6/1000  = 3/500

The value of line AL is 21. 51cm

Let's start by finding line AB using

Sin α = opposite/ hypotenuse

Sin 90 = x/ 24

1 = x/24

Then, cross multiply

We have line AB = 24cm

Now, let's find line AC

Sin angle B = line AC/24

Let's find angle B

We know that angle A + angle B + angle C = 180

But angle B = 2 Angle A

x + 2x + 90 = 180

3x + 90 = 180

3x = 180-90

x = 30°

Then Angle B = 2 × x = 2 × 30 = 60°

Sin 60 = x/ 24

0. 8660 = x/24

Cross multiply

x = 24 × 0. 8660

x = 20. 78cm

From the diagram, we have the angle of A  in the given triangle to be divide into two by the bisector, angle A = 15°

To find line AL, let's use

Cos α = adjacent/ line AL

Cos 15 = 20. 78/ line AL

Line AL = 20. 78/ cos 15

Line AL = 20. 78 / 0. 9659

Line AL = 21. 51 cm

Thus, the value of line AL is 21. 51cm

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The number that completes the System of Linear Inequalities represented by the Graph y >= 2x – 2 and x + 4y > =  is -12. Hence, x + 4y [tex]\geq[/tex] -12

A collection of linear inequalities in the same variables is referred to as a system of linear inequalities. Any ordered pair that fulfills all of the inequalities is the solution.

Recall that:

y = mx + c

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

Given that

The orange line intersects y-axis at (0,-2), therefore the y-intercept is -2.

The orange line intersect the points that are (1,0)  and (0, -2).

The slope of the line can be obtained as follows:

m = (-2-0)/(0-1)

= -2/-1

= 2

The slope of the line is m = 2.

Therefore, the orange line is y [tex]\geq[/tex] 2x -2

The blue line intersects y-axis at (0,-3), therefore the y-intercept is -3.

The blue line intersect the points that are (-4, -2) and  (0, -3)

The slope of the line can be obtained as follows.

m = (-3-(-2))/(0-(-4))

= (-3 + 2)/4

= - (1/4)

The slope of the line is:
m = -(1/4)

The inequalities is x + 4y [tex]\geq[/tex] b passes through the point (0, -3)

(0) + 4 (-3) = b

-12 =b

Thus, -12 in is the number that completes the system. Hence, x + 4y [tex]\geq[/tex] -12

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Answer:

it should be fine, but it can also depend on the quality of the wig

Step-by-step explanation: