Solve for x: 4/7 = x-1/12

There are two ways to solve this problem from the given situation. I'll type out both to help give you a better understanding of this problem.

Method 1: Straightforward, yet complicated

The shaded trapezoid has two base lengths of 25 mm and 50 mm, with a height of 35 mm.

The formula for the area of a trapezoid is the following:

[tex]A=\dfrac{a+b}{2}*h[/tex]

Where a and b are the base lengths and h is the height. Substitute the dimensions of the trapezoid and the formula changes to:

[tex]= \dfrac{25+50}{2}*35[/tex]

Simplifying the equation give us:

[tex]=\dfrac{2625}{2}[/tex]

[tex]=1312.5[/tex]

The trapezoid has an area of 1312.5 mm²

Method 2: Abstract, yet simple

The parallelogram is made up from 2 congruent trapezoids, and one of them is shaded. Thus, we just need to find the area of the parallelogram and divide it by 2 to get the area of a single trapezoid, which will give us the area of the shaded region.

The area formula of a parallelogram is simple, base times height.

The base is 25+50, or 75 mm. The height is 35 mm.

Multiplying these two values gives us 2625 mm². Dividing this by 2 gives us 1312.5 mm². That's the area of a single trapezoid (half the parallelogram), which should also be the area of the shaded region.

This is the same answer we got from method 1.

Conclusion:

The answer is 1312.5 mm²

Both methods give the same answer, which means they each make sure that the other is correct. Let me know if you need any clarifications, thanks!

~ Padoru

Answer: Brownies that are $1.58 for a 6-pack

Step-by-step explanation:

Well, since 6 times 2 is 12, why don’t you just add $1.58 again, right? So if you do you get $3.16. So Brownies that are $1.58 for a 6-pack are better.

Answer:

Step-by-step explanation:

First you divide 1.58 and 6 to find how much one brownie is.

So that would be roughly $0.26.

Now you divide 3.99 and 12 which is roughly $0.33.

So you now have to see which one has a smaller cost. Which is $0.26. SO it would be the 6-pack.

Another way to figure is out to multiply 0.26 and 12, and 0.33 and 6.

0.33 x 6=1.98

0.26 x 12=3.12

So that makes it more clear that the 6 pack is a better buy!

A total of 168 non-commercial vehicles and 60 commercial vehicles use the country's highways during September.

Step-by-step explanation:

Step 1:

Assume the number of non-commercial vehicles to be x and the number of commercial vehicles to be y.

It is given that for every 14 non-commercial vehicles there will be 5 commercial vehicles. So a ratio can be formed as follows;

[tex]\frac{x}{14}[/tex] = [tex]\frac{y}{5}[/tex], cross multiplying, we get [tex]5 x=14 y[/tex], take this as equation 1.

Step 2:

It is also given that there were 108 more non-commercial vehicles than commercial vehicles. So

[tex]x=y+108[/tex], take this as equation 2.

If we solve equations 1 and 2, we will get the values of x and y.

Step 3;

Substitute equation 2 in equation 1.

[tex]5(y+108)=14 y[/tex],

[tex]5y+540 = 14y[/tex],

[tex]y = \frac{540}{9} = 60[/tex].

Substitute [tex]y = 60[/tex] in equation 2.

[tex]x=60+108 = 168[/tex].

So x = 168 and y = 60.

So a total of 168 non-commercial vehicles and 60 commercial vehicles use the country's highways during September.

Answer:

b

Step-by-step explanation:

when you have the l-10l  it means the distance from 0  and the distance from 0 from -10 is 10

Answer:

= 12 square units

Step-by-step explanation:

Please look at the photo attached below, I think it is fit with your question

To find the area, substitute the values given in the question into the formula given below.

Area = base • height

= x • h

= 3 units • 4 units

= 12 square units

Answer:

the answer is 24

Step-by-step explanation:

because if you are in study island it says 24

Step-by-step explanation:

x=y

y=1/z^3

Now,

for equation,

x=y=1/z^3

x is directly proportional to y and is inversely proportional to the cube of z.

Then, x = y = [tex]$\frac{1}{z}^{3[/tex].

If y exists directly proportional to x then,

y/x = k

⟹ y = kx

If y exists inversely proportional to x then,

yx = k

⟹ y = k/x

Let, x is directly proportional to y.

It suggests that when all other phrases which affect x exist kept constant, x changes at a rate that exists a constant multiple of the rate at which y changes.

Let, x ∝ y

⟹ x = ky, x ∝ y

⟹ x = ky

Where k is constant.

when you exist told that x exists directly proportional to y.

x = y

y = [tex]$\frac{1}{z}^{3[/tex]

From the given information, we get

x = y = [tex]$\frac{1}{z}^{3[/tex]

Here, x is directly proportional to y and is inversely proportional to the cube of z.

Therefore, x = y = [tex]$\frac{1}{z}^{3[/tex].

To learn more about directly proportional and inversely proportional

https://brainly.com/question/1266676

#SPJ2

Answer:

20[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Simplify

[tex]\sqrt{8}[/tex] = [tex]\sqrt{4(2)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{2}[/tex] = 2[tex]\sqrt{2}[/tex]

Thus

6[tex]\sqrt{8}[/tex] + 8[tex]\sqrt{2}[/tex]

= 6(2[tex]\sqrt{2}[/tex] ) + 8[tex]\sqrt{2}[/tex]

= 12[tex]\sqrt{2}[/tex] + 8[tex]\sqrt{2}[/tex]

= 20[tex]\sqrt{2}[/tex]

Answer: Alonso has $7 and Rico has $700

Step-by-step explanation:

Kendra= 70$

Alsonso= 70 * 0.1 = 7$

Rico= 70 *10 = 700$

please give brainliest!

Answer:Alonso has $7 and Rico has $700

Step-by-step explanation:

Kendra= 70$

Alsonso= 70 * 0.1 = 7$

Rico= 70 *10 = 700$

please give brainliest!

Answer:

3/10

Step-by-step explanation:there are 10 marbles all together three blue ones

Answer:

[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

You have 3 possibilities to get a blue marble out of 10

Answer:

211

Step-by-step explanation:

952 + 1520 then divide by 12

Answer:

x = 2

Step-by-step explanation:

Step 1:  Convert words into an expression

What is the value of x in the equation 13 x minus 2 (8 + 5 x) = 12 minus 11 x?

13x - 2(8 + 5x) = 12 - 11x

Step 2:  Distribute

13x - 2(8 + 5x) = 12 - 11x

13x - 16 - 10x = 12 - 11x

Step 3:  Solve for x

13x - 16 - 10x + 11x + 16 = 12 - 11x + 11x + 16

14x / 14 = 28 / 14

x = 2

Answer:  x = 2

Answer:

x=2

Step-by-step explanation:

Just took the test

Answer:

(20+2) (20-2) = 20² - 2²

20² - 2² = 396

Step-by-step explanation:

from the rule of the difference of two square which states thate

       (a + b)(a − b) = a² − b²

therefore, 22 can also be written as (20 + 2),

while 18 can be written as (20 -2)

therefore by the rule of the difference of two square the product of both expression will give

      (20+2) (20-2) = 20² - 2² = 400 - 4 = 396

Step-by-step explanation:

= (20 + 2) × (20 - 2)

= 22 × 18

= a^2 - b^2 = 396

= (a + b) × (a - b) = 396

From the above, a = 20 and b = 2.

Therefore,

(20^2) - (2^2) = 396.

Answer:

the answer is 36xy squared

He needs to drink 3 cups MORE to meet his daily requirement.

Step-by-step explanation:

Here, as given in the question:

The total need for water = half a gallon = 0.5 gallon

1 gallon  = 128 oz

So, 0.5 gallon = 128/2  = 64 oz

Now, the capacity of 1 cup = 3.5 oz

The number of cups already drank by the person = 15 cups

So, the total amount of water already taken by him

= 15 cups x Capacity of 1 cup

= 15 x (3.5 oz)  = 52.5 oz

So, the amount of water left to be drink by him

= Total Need - Already covered

= 64 oz - 52 . 5 oz  =  11.5 oz

Now, as 1 cup = 3.5 oz

So, 11.5 oz  has [tex]( \frac{11.5}{3.5} )[/tex]cups  = 3.28 cup≈ 3 cups

Hence, he needs to drink 3 cups MORE to meet his daily requirement.

Final answer:

Abby has already consumed 52.5 oz of water by drinking 15 small cups at 3.5 oz each. Since the recommended daily intake is 64 oz, she needs to drink an additional 11.5 oz to meet the daily hydration recommendation.

Explanation:

The question pertains to calculating the amount of water a person needs to drink to meet the recommended daily hydration level. In this case, the student needs to find out how much more water Abby should drink after having consumed 15 cups of 3.5 oz each.

First, we calculate the total amount of water Abby has already consumed -

Therefore, Abby needs to drink an additional 11.5 ounces of water to meet the daily recommendation of half a gallon.

Answer:

$13,200

Step-by-step explanation:

1,100/100 is 11

1200*11=13,200

Answer:

The contractor charges $13,200

For 1,100 square feets

Step-by-step explanation:

To solve the problem we need to understand how to charges

Step one

Given

For each 100 square feet of roofing he charges $1,200

Hence for 1,100 square feet we can see that the charges is 11times

This is because 1100/100= 11

Step two :

Hence he charges 11 times more

Therefore his fee for 1,100 square feet is

1200*11=$13,200

Answer: It's B

Step-by-step explanation: Got 100% on the quiz

Solution:

The slope intercept form of equation is given as:

y = mx + c ------ eqn 1

Where,

m is the slope of line

c is the y intercept

From given,

slope = m = 3

y intercept = c = 5

Substitute m = 3 and c = 5 in eqn 1

y = 3x + 5

3x - y = -5

Thus the equation of line is found

Answer:

48.

Step-by-step explanation:

Perimeter is 2l+2w

current perimeter is 16

16x3=48

Answer:

16'.

Step-by-step explanation:

A square has 4 equal  sides so it is 4 * 4' = 16'.

The options A, B and C are geometric sequences whereas option D is not.

Step-by-step explanation:

Step 1:

For a series to be a geometric sequence, the numbers in the series must be of a common multiplying ratio. So multiplying a constant value with any number will give the value of the next number.

The multiplying constant can be determined by;

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{3^{rd} term}{2^{nd} term} = \frac{4^{th} term}{3^{rd} term} =[/tex]  The common multiplying ratio.

Step 2:

For option A, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{10}{5} =2,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{20}{10} =2, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{40}{20} =2.[/tex]

Since there is a common multiplying ratio of 2, option A is a geometric series.

Step 3:

For option B, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{5}{10} =0.5,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{2.5}{5} =0.5, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{2.5}{1.25} =0.5.[/tex]

Since there is a common multiplying ratio of 0.5, option B is also a geometric series.

Step 4:

For option C, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{3}{1} =3,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{9}{3} =3, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{27}{9} =3.[/tex]

Since there is a common multiplying ratio of 3, option C is a geometric series.

Step 5:

For option D, we determine the multiplying ratio,

[tex]\frac{2^{nd} term}{1^{st} term} = \frac{6}{3} =2,[/tex]  [tex]\frac{3^{rd} term}{2^{nd} term} = \frac{9}{6} =1.5, and[/tex] [tex]\frac{4^{th} term}{3^{rd} term} = \frac{12}{9} =1.33.[/tex]

Since there is no common multiplying ratio, option D is not a geometric series.

Answer: C & D

Step-by-step explanation:

The length of image of AB after the dilation is 18 cm

Solution:

Given data:

Length of AB = 9 cm

Scale factor (k) = 2

Length of image of AB = ?

By the definition of scale factor,

[tex]$k=\frac{\text { Length of Dilated image AB }}{\text { Length of original image } \mathrm{AB}}$[/tex]

[tex]$2=\frac{\text { Length of Dilated image AB }}{9}[/tex]

Do cross multiplication, we get

2 × 9 = Length of dilated image of AB

18 = Length of dilated image of AB

Hence the length of image of AB after the dilation is 18 cm.

Answer:

x= 45

y= 18.5 (3 s.f.)

Step-by-step explanation:

Since the quadrilateral has 4 equal sides, it is a square and hence the 4 angles are right angles.

I have drawn the 2 triangles of the square separately for better understanding.

Please see the attached pictures for full solution.

Answer:

70

Step-by-step explanation:

Step 1:  Divide

420 / 670

70

Answer:  70

Answer:

19,200 square feet

Step-by-step explanation:

Step-by-step explanation:

Denominators of both the fractions are 2x and (x - 5)

Therefore,

Lowest common denominator

[tex]= 2x \times (x - 5) \\

= 2 {x}^{2} - 10x[/tex]

Answer:

10  2/3

Step-by-step explanation:

Multiply 16 by 2/3

2/3 *16

32/3

Change the improper faction to a mixed number

10 2/3 of an ounce

Answer:

10.666 Ounces

Step-by-step explanation:

16 Ounces ÷ 3 = 5.333 Ounces

5.333 Ounces × 2 = 10.666 Ounces

Option B:

[tex]$x=\pm 2\frac{1}{2}[/tex]

Solution:

Given expression:

[tex]$3 x^{2}=18 \frac{3}{4}[/tex]

To find the value of x:

[tex]$3 x^{2}=18 \frac{3}{4}[/tex]

Convert mixed fraction into improper fraction.

[tex]$3 x^{2}= \frac{18\times 4+3}{4}[/tex]

[tex]$3 x^{2}= \frac{75}{4}[/tex]

Divide by 3 on both sides of the equation, we get

[tex]$x^{2}= \frac{25}{4}[/tex]

[tex]$ x^{2}= \frac{5^2}{2^2}[/tex]

Taking square root on both side of the equation.

[tex]$\sqrt{ x^{2}}= \sqrt{\frac{5^2}{2^2}}[/tex]

[tex]$ x=\pm \frac{5}{2}[/tex]

Convert improper fraction into mixed fraction.

[tex]$x=\pm 2\frac{1}{2}[/tex]

Hence option B is the correct answer.