Lee can frame a cabin in 4 days less than Ron. When they work together, they will do the job in 4 days. How long would each of them take to frame the cabin alone?

we have

m∠P=[tex](2x)\°[/tex]

m∠Q=[tex](4x)\°[/tex]

m∠R=[tex](6x)\°[/tex]

1) By the triangle sum theorem, the sum of the angles in a triangle is equal to [tex]180\°[/tex]

therefore

m∠P+m∠Q+m∠R=[tex]180\°[/tex]

we know that

Substitution Property of Equality, states that If the values of two quantities are known to be equal, you can replace the value of one quantity with the other

so

2) Using the Substitution Property of Equality

[tex](2x)\°+(4x)\°+(6x)\°=180\°[/tex]

Simplifying the equation gets

[tex](12x)\°=180\°[/tex]

3) using the division property of equality

The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the sides remain equal

[tex](12x)\°/12=180\°/12[/tex]

[tex]x=15\°[/tex]

therefore

the answer is

Part a) Substitution Property of Equality

Part b)  [tex]x=15\°[/tex]

Answer:

Part a) Substitution Property of Equality

Part b) x=15

Step-by-step explanation:

Given triangle PQR with

[tex]m\angle P=(2x)^{\circ}[/tex]

[tex]m\angle Q=(4x)^{\circ}[/tex]

[tex]m\angle R=(6x)^{\circ}[/tex]

By the triangle sum property, the sum of the angles of a triangle is equal to [tex]180^{\circ}[/tex]

∴ m∠P+m∠Q+m∠R=180°

Substitution Property of Equality, states that If the values of two quantities are known to be equal, one can replace the value of one quantity with the other

[tex](2x)^{\circ}+(4x)^{\circ}+(6x)^{\circ}=180^{\circ}[/tex]

Simplifying the equation we get

[tex](12x)^{\circ}=180^{\circ}[/tex]

Using the division property of equality

The Division Property of Equality states that division with the same non zero number results that both sides remain equal

[tex]\frac{(12x)^{\circ}}{12}=\frac{180^{\circ}}{12}[/tex]

[tex]x=15[/tex]

Hence, the answer is

Part a) Substitution Property of Equality

Part b) x=15

Answer:

20 and 30. that's your answer.

Step-by-step explanation:

x + y ≥ 20 ( total number of shirts at least 20)

15x + 10y ≤ 250 ( total amount spent no more than $250)

These are the answers.

3. x + y ≥ 20 

5. 15x + 10y ≤ 250 

Hope this helps and have a wonderful day!

An equation that is true for all real numbers for which the operations are defined is called an identity. It is always true no matter the values of its variables. An example is sin²(x) + cos²(x) = 1

An equation that is true for all real numbers for which both sides are defined is called an identity. An identity equation is always true, no matter what values are substituted for its variables. For example, the equation sin²(x) + cos²(x) = 1 is an identity because it is valid for all real numbers x.

Identity equations commonly appear in branches of math such as algebra and trigonometry.

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Answer:

Daily Payment = 5h+8

Step-by-step explanation:

Here we are given that in seven days the amount Harriet earned is given as

35h+56

It is also given that the amount earned each day is same.

We have to determine the amount earned each day. Total number of days is 7 . Hence in order to find the daily earning we divide the total earning by 7

Daily earning =

[tex]E=\frac{35h+56}{7}\\E=\frac{7(5h+8)}{7}\\E=5h+8[/tex]

Hence answer is 5h+8

Answer:

The common ratio is  [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Given sequence,

27, 9, 3, 1

Since,

[tex]\frac{9}{27}=\frac{3}{9}=\frac{1}{3}[/tex]

Hence, in the given sequence the ratio of a term to its previous term is [tex]\frac{1}{3}[/tex]

Therefore, we can say that,

The common ratio of the given sequence is [tex]\frac{1}{3}[/tex]

The number of different ways this order can be filled is:

                              13 ways.

A customer ordered fourteen zingers.

zingers are placed in packages of​ four, three, or one.

Case-1

If the number of packages of four are: 3

Then 4×3=12 zingers.

a)

So, there will be zero packet of 3.

and 2 packs of 1.

Since, 12+2×1=14

Case-2

If the number of packages of four are: 2

i.e. 4×2= 8 zingers.

a)

If number of packages of 3 are: 2

i.e. 3×2=6

then number of package of 1 have to be 0.

b)

If number of packages of 3 are: 1

i.e. 3×1=3 zingers

Number of packages of 1 zinger will be: 3

i.e. 8+3+3=14

c)

If number of packages of 3 are: 0

Then number of packets of 1 will be:  6

Case-3

If the number of packages of four are: 1

a)

If number of packages of 3 are: 3

i.e. 3×3=9 zingers.

Hence, number of packets of 1 have to be: 1

b)

If number of packages of 3 are: 2

i.e. 3×2=6 zingers

Then number of packets of 1 have to be: 4

c)

If number of packages of 3 are: 1

i.e. 3×1=3 zingers

Then number of packets of 1 have to be: 7

d)

If number of packages of 3 are: 0

i.e. 3×0=0 zingers

Then number of packets of 1 have to be: 10

Case-4

If the number of packages of four are: 0

a)

If number of packages of 3 are: 4

i.e. 3×4=12 zingers

Then number of packets of 1 have to be: 2

b)

If number of packages of 3 are: 3

i.e. 3×3=9 zingers

Then number of packets of 1 have to be: 5

c)

If number of packages of 3 are: 2

i.e. 3×2=6 zingers

Then number of packets of 1 have to be: 8

d)

If number of packages of 3 are: 1

i.e. 3×1=3 zingers

Then number of packets of 1 have to be: 11

e)

If number of packages of 3 are: 0

i.e. 3×0=0 zingers

Then number of packets of 1 have to be: 14

There are total 13 ways of doing so.

( 1 from case-1

3 from case-2

4 from case-3

and 5 from case-4

i.e.  1+3+4+5=13 ways )

The order can be filled in 5 different ways by using packages of 4, 3, or 1 zingers.

To find the number of different ways the order can be filled, we can use the concept of permutations and combinations. Since zingers can be placed in packages of 4, 3, or 1, we need to find all the possible combinations of these packages that add up to 14.

Therefore, the total number of different ways the order can be filled is 2 + 2 + 1 = 5.

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Answer:

The ball will land inside the goal.

Step-by-step explanation:

Given : The flight of the ball is modeled by a parabola.

To find : Will the soccer ball land in the goal?

Solution :

Let the equation of the parabola be,

[tex]y=a(x-h)^2+k[/tex]

Where, (h,k) are the vertex of the parabola,

According to question,

A soccer player who is 27 feet from a goal.

Let A be the point where player stand i.e, (27,0)

The height of the goal is 8 feet.

Let B be the point of height of goal i.e, (0,8)

The ball reached a maximum height of 10 feet when it was 15 feet from the soccer player.

The distance from goal to the distance 15 feet away from the player is

27-15=12 feet

Let C be the point with maximum height i.e, (12,10)

C is the vertex of the parabola and A is the point on the parabola.

Then, The equation of parabola is

[tex]y=a(x-12)^2+10[/tex]

Point A satisfy the equation,

[tex]0=a(27-12)^2+10[/tex]

[tex]0=a(15)^2+10[/tex]

[tex]a=-\frac{10}{225}[/tex]

Substitute back in equation,

[tex]y=-\frac{10}{225}(x-12)^2+10[/tex]

Now, we find the y-intercept of the equation i.e, x=0,

[tex]y=-\frac{10}{225}(0-12)^2+10[/tex]

[tex]y=-\frac{10}{225}(144)+10[/tex]

[tex]y=3.6[/tex]

If the y-intercept is greater than 8 then the ball will land outside the goal.

If the y-intercept is less than 8 then the ball will land inside the goal.

As 3.6<8

Therefore, The ball will land inside the goal.

Refer the attached figure below.

Final answer:

The soccer ball will not land in the goal due to its maximum height being above the height of the goal.

Explanation:

To determine if the soccer ball will land in the goal, we need to analyze its flight path. From the given information, we know that the ball reached a maximum height of 10 feet when it was 15 feet from the soccer player. This indicates that the ball's flight path is modeled by a downward-opening parabola.

Since the soccer player is 27 feet from the goal, we can consider the ball's horizontal distance from the player to the goal as the x-coordinate, and its height above the ground as the y-coordinate.

Based on the given information, the soccer ball will not land in the goal. The ball's maximum height is 10 feet, but the goal has a height of 8 feet. This means that at any point along its flight path, the ball's height will be above the height of the goal.

Final answer:

The expression log3 6 can be converted to a logarithm of base 2 using the change of base formula, which results in log2 6 / log2 3. So the correct option is b.

Explanation:

The student asked how to express log3 6 as a logarithm with a base of 2. To perform this conversion, we can use the change of base formula, which states that logab = logcb / logca for any positive numbers a, b, and c, where a and c are not equal to 1. In this formula, 'c' can be any base, but in our case, we will use base 2 since that's what the question requires.

So, by applying the change of base formula, we can write:

Therefore, the correct option that represents log3 6 as a logarithm of base 2 is:

A = B+32

B = 5C

A = 5C+32

C has d dollars so replace d for c

A = 5d+32

Final answer:

The base of the triangle is 8 inches, one side is 12 inches (base + 4), and the other side is 14 inches (base + 6). Hence, the side lengths of the triangle are 8 inches, 12 inches, and 14 inches, with a total perimeter of 34 inches.

Explanation:

The question describes a triangle with sides of varying lengths relative to what is defined as the base of the triangle. To find the length of each side, we'll use algebra and the fact that the perimeter of the triangle is given as 34 inches.

Let's denote the base as b. According to the problem, one side is 4 inches longer than the base, which would be b + 4 inches. The third side is 6 inches longer than the base, which would be b + 6 inches. The perimeter of a triangle is the sum of all its sides, so we have:

b + (b + 4) + (b + 6) = 34

Combining like terms, we get:

3b + 10 = 34

Subtracting 10 from both sides gives us:

3b = 24

Dividing by 3 gives us the length of the base:

b = 8 inches

Now, we can find the lengths of the other two sides:

b + 4 inches is 12 inches and b + 6 inches is 14 inches.

So, the lengths of the sides of the triangle are 8 inches, 12 inches, and 14 inches.

The slope of the line passing through points is undefined.

The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.

For the given situation,

The line passing through points (x1, y1) is (-6, 3) and (x2,y2) is (-6, 39)

The formula of slope of line is

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

⇒ [tex]m=\frac{39-3}{-6-(-6)}[/tex]

⇒ [tex]m=\frac{39-3}{-6+6}[/tex]

⇒ [tex]m=\frac{39-3}{0}[/tex]

⇒ [tex]m=\infty[/tex]

Since x1 = x2, there is no horizontal change. The line passes as a straight line.

Hence we can conclude that the slope of the line passing through points is undefined.

Learn more about slope of a line here

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Answer:

1.49

Step-by-step explanation:

50% of 2.98 is 1.49

Answer:

Distribute 2 inside the parenthesis

Step-by-step explanation:

Julie started solving the equation

3x=4+2(3−x)

To simplify any expression we use order of opeation PEMDAS

Always start simplifying the parenthesis

To remove parenthesis we apply distributive property

Distribute 2 inside th4e parenthesis

3x=4+2(3−x)

3x=4+6-2x

So next step is distributing 2 inside the parenthesis

3x=4+6-2x

Answer:

I would think the answer is "axioms are used to prove theorems"

Step-by-step explanation:

According to the given statement, we can get the equation:

50 - 3x = 1/2 (50-x)

where x = amount removed from bag two, 3x removed from bag one

Then we multiply both sides by 2 (to eliminate the ½)

100-6x= 50-x

Add 6x to both sides

100= 50-5x

Then subtract 50 from both sides

50=5x

Lastly, divide by 5

10=x

Therefore 10 kg of sugar was removed from bag 2

further, 3x= 30, so 30 kg of sugar was removed from bag 1.

50-30=20 kg remaining in bag 1.

50-10=40 kg remaining in bag 2.

Answer:

40 kg in the first bag, 80 in the second

Step-by-step explanation: