2/67 = 18/x
..............................................................................................................................................................

Answer:

60.42

Step-by-step explanation:

tan40 = opposite/adjascent

tan40 =x/72

x=72tan40

x = 72 * 0.8391

x = 60.42

It will take 4 years for these trees to be the same height

Step-by-step explanation:

A gardener is planting two types of trees:

Type A is 6 feet tall and grows at a rate of 12 inches per year

Type B is 2 feet tall and grows at a rate of 24 inches per year

We need to find exactly how many years it will take for these trees to be the same height

Assume that it will take x years for these trees to be the same height

Type A:

∵ The initial height of the tree is 6 feet

∵ 1 foot = 12 inches

∴ 6 feet = 6 × 12 = 72 inches

∴ The initial height of the tree is 72 inches

∵ It grows at a rate of 12 inches per year

∵ The number of years is x

∴ The height of the tree in x years = 72 + 12 x

Type B:

∵ The initial height of the tree is 2 feet

∴ 2 feet = 2 × 12 = 24 inches

∴ The initial height of the tree is 24 inches

∵ It grows at a rate of 24 inches per year

∵ The number of years is x

∴ The height of the tree in x years = 24 + 24 x

Equate The heights of the two types

∴ 72 + 12 x = 24 + 24 x

- Subtract 2 from both sides

∴ 48 + 12 x = 24 x

- Subtract 12 x from both sides

∴ 48 = 12 x

- Divide both sides by 12

∴ x = 4

It will take 4 years for these trees to be the same height

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The price of jacket was $24.54

Step-by-step explanation:

Let,

Cost of jacket = x

Cost of pair of shoes = y

According to given statement;

x+y=52.95   Eqn 1

x = y-3.87    Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex](y-3.87)+y=52.95\\y-3.87+y=52.95\\2y=52.95+3.87\\2y=56.82\\[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{56.82}{2}\\y=28.41[/tex]

Putting y=28.41 in Eqn 2,

[tex]x=28.41-3.87\\x=24.54[/tex]

The price of jacket was $24.54

Keywords: linear equation, division

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Final answer:

The price of the jacket is $24.54, calculated by first finding the price of the shoes from the total cost and the price difference between the jacket and shoes, and then subtracting the difference from the price of the shoes.

Explanation:

The question at hand involves finding the price of a jacket given the total cost of the jacket and a pair of shoes and the relationship between their prices. Let's denote the price of the jacket as J and the price of the shoes as S. According to the information provided, we have the following two equations:

J + S = $52.95 (The total cost of both items)

J = S - $3.87 (The jacket costs $3.87 less than the shoes)

We can substitute the second equation into the first to find the price of the shoes:

(S - $3.87) + S = $52.95

2S - $3.87 = $52.95

2S = $52.95 + $3.87

2S = $56.82

S = $56.82 / 2

S = $28.41

Now we can find the price of the jacket by substituting the price of the shoes back into the second equation:

J = $28.41 - $3.87

J = $24.54

Therefore, the price of the jacket is $24.54.

Answer:

The answer is y = 6.

Step-by-step explanation:

Given:

RS = [tex]3y+41[/tex], ST = [tex]18y-76[/tex] and RT = 91.

Now, to find the [tex]y[/tex].

According to question add the equations:

RS + ST = RT

[tex]3y+41+18y-76=91[/tex]

Adding the numbers and variables in L.H.S.

[tex]3y+18y-76+41=91[/tex]

[tex]21y-35=91[/tex]

Adding 35 on both sides:

[tex]21y-35+35=91+35[/tex]

[tex]21y=126[/tex]

Dividing both sides by 21:

[tex]21y\div 21=126\div 21[/tex]

[tex]y=6[/tex]

Therefore, the answer is y = 6.

1140

Step-by-step explanation:

The algebraic expression of "3 times the sum of 2 and y" is 3(2 + y) ⇒ 1st answer

Step-by-step explanation:

Let us revise some words in the operations of mathematics problems

∵ The algebraic expression is " 3 times the sum of 2 and y "

∵ Sum is the answer of add

∴ add 2 and y

∴ The sum of 2 and y = 2 + y

∵ 3 times means multiply by 3

∴ 3 times the sum

∴ Multiply the sum by 3

∵ The sum = 2 + y

∴ Multiply (2 + y ) by 3

∴ 3(2 + y)

∴ 3 times the sum of 2 and y = 3(2 + y)

The algebraic expression of "3 times the sum of 2 and y" is 3(2 + y)

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Answer:

a

=

Step-by-step explanation:

uo[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

Answer:

x=1, y=1. (1, 1). The answer is D).

Step-by-step explanation:

3x-5y=-2

4x-7y=-3

--------------

4(3x-5y)=4(-2)

-3(4x-7y)=-3(-3)

------------------------

12x-20y=-8

-12x+21y=9

--------------------

y=1

3x-5(1)=-2

3x-5=-2

3x=-2+5

3x=3

x=3/3

x=1

Answer:

not direct variation

Step-by-step explanation:

The equation for x and y in direct variation is

y = kx ← k is the constant of variation

y = [tex]\frac{5}{x}[/tex] is not in this form, thus not direct variation.

The equation for x and y varying inversely is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

y = [tex]\frac{5}{x}[/tex] is in this form and represents inverse variation

Answer:

m = - 1

Step-by-step explanation:

Given

[tex]\frac{15m+3}{2}[/tex] = - 6

Multiply both sides by 2 to clear the fraction

15m + 3 = - 12 ( subtract 3 from both sides )

15m = - 15 ( divide both sides by 15 )

m = - 1

[tex]\text{Solve:}\\\\\frac{15m+3}{2}=-6\\\\\text{Multiply both sides by 2}\\\\15m+3=-12\\\\\text{Subtract 3 from both sides}\\\\15m=-15\\\\\text{Divide both sides by 15}\\\\\boxed{m=-1}[/tex]

Answer:

Step-by-step explanation:

1. 1 7/9

2. 22

3. 8

4. 64

5. 16

Answer:

Cube root of 16

Step-by-step explanation:

Place 2 inside of the square root and 3 outside and 4 inside

Here's how it looks:

[tex]\sqrt[3]{2} ^{4}[/tex]

then you can quadruple root the 2 which gives you 16 and 16 doesn't simplify any further into a cube root so your answer is the cube root of 16

Answer:

1. Ox-intercept is -4; y-intercept is 8.

2. Ox-intercept is 16; v-intercept is 20.

Step-by-step explanation:

1. -10x + 5y = 40

Recall the equation of line in slope - intercept form :

y = mx + c , where m is the slope and c is the y - intercept

Writing the given equation in this form,we have:

-10x + 5y = 40

5y = 10x + 40

y = 10/5 x + 40/5

y = 2x + 8

comparing with y = mx +c , then y - intercept is 8 , the x - intercept is the point at which y = 0 , substituting y = 0 into the equation , we have

0 = 2x + 8

2x = -8

x = -8/2

x = -4

2. Following the same procedure:

y = -5x/4 + 20

y - intercept = 20

x - intercept = 16

The homing pigeon will minimize its flying time by flying straight across the river, then directly to its nest. The time to fly this route would be 142.5 seconds.

The homing pigeon's path that will minimize its flying time would-be one where it flies straight across the river and then flies directly to its nest. The total time can be calculated by adding the time it flies over water and the time it flies over land. Initially, calculating the flying time over water, if the river is 500 meters wide, the time will be the distance divided by speed which equals 500m/8m/s = 62.5s . Now the land distance is the total distance minus the width of the river, so it would be 1300m – 500m = 800m. The time to cross this distance will be 800m/10m/s = 80s. Hence, adding both times, total flying time will be 62.5s + 80s = 142.5s. Therefore, the shortest path is firstly, flying straight across the river, and then straight towards its nest.

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Answer:

8

Step-by-step explanation:

Answer:

The answer is C.

Step-by-step explanation:

Just failed hah stream fancy

Answer:

Answer is a^8/b^10

Option C

Step-by-step explanation:

((a²b-³)/(a-²b²))² where b and a are not equal zero

To solve this equation we start solving the equation from inside the bracket. And for simplicity we solve the numerator and solve the denominator before dividing them with each other. Now let get started

((a²b-³)/(a-²b²))²

Recall from indices that

a ^ -b = 1/a^b

I.e b-³ = 1/b³... We will apply this here.

((a²b-³)/(a-²b²))²

=((a²* 1/b³)/(b²*1/a²))²

=((a²/b³)/(b²/a²))²

Also recall that

(a/b) / (c/d) = (a/b) * (d/c)

Therefore

=((a²/b³)/(b²/a²))²

=(a²/b³ * a²/b²)²

Recall that: a^b * a^c = a^(b+c)

= (a ^ (2+2) / b ^ (2+3))²

= (a^4/b^5)²

Recall that: (a^b)^c = a^(b+c)

Therefore:

=™(a^4/b^5)²

=(a^(4*2)/b^(5*2))

= a^8/b^10

Answer:

The diameter of the pizza is 12 inches

Step-by-step explanation:

Given:

Circumference of a pizza = 38 inches

To Find:

The Diameter of the pizza =?

Solution:

Circumference:

The distance around the edge of a circle (or any curvy shape). It is a type of perimeter.

We know that the shape of the pizza is circle.

So the given circumference is circumference of a circle.

Now,

Circumference of the circle(pizza)=[tex]2\pi r[/tex]

where r is the radius of the circle

circumference of the pizza =38

Thus

[tex]2\pi r= 38[/tex]

[tex]\pi r=\frac{38}{2}[/tex]

[tex]\pi r=19[/tex]

[tex]r=\frac{19}{3.14}[/tex]

r=6.050 inches

Now,

Diameter = [tex]2\times r[/tex]

Diameter = [tex]2\times 6.05[/tex]

Diameter=12.1 inches

Rounding to the nearest tenth

Diameter=12 inches

Final answer:

To find the diameter of a pizza with a circumference of about 38 inches, we apply the formula C = πD, leading to a calculation of 38 / 3.14, which results in approximately 12.1 inches.

Explanation:

The question is about finding the diameter of a pizza given its circumference, which is approximately 38 inches. To calculate the diameter from the circumference, we use the formula C = πD, where C is the circumference and D is the diameter. Since π (Pi) is approximately 3.14, we rearrange the formula to find the diameter: D = C / π. Thus, substituting the given value of C = 38 inches, we get D = 38 / 3.14, which is approximately 12.1 inches.

With 2.5 litres of water, it can be estimated that you can make 400 grams of pasta.

The question is asking how many grams of pasta could be made with 2.5 litres (or 2500 ml) of water. According to the initial ratio, 500 ml of water is used to make 80 grams of pasta.

To find out how many grams of pasta can be made with 2.5 liters of water, you first need to find the pasta-to-water ratio which is 80 grams pasta to 500 ml water, or 0.16 grams/ml. You then multiply this ratio by the total amount of water you have:

0.16 grams/ml * 2500 ml = 400 grams of pasta.

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Answer:

1

Step-by-step explanation:

Using the rule of exponents

[tex]a^{0}[/tex] = 1

Any expression raised to the power of zero will equal 1

Given

[tex](3/7)^{0}[/tex] = 1

Answer:4.6

Step-by-step explanation:

28/6

Answer:

168/35 points per minute

Step-by-step explanation:

5 5/6=35/6

28/(35/6)=(28/1)(6/35)=168/35

Answer:

53%

Step-by-step explanation:

subtract 6.5 - 4.25 = 2.25

then divide 2.25/4.25 = .529

times answer by 100 = 53% rounded

Answer: 53% increase

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

Work Shown:

A = old value = 4.25

B = new value = 6.50

C = percent change

C = 100*(B-A)/A

C = 100*(6.50 - 4.25)/4.25

C = 52.94%

C = 53%

------------

notes:

The positive C value indicates we have a percent increase. If C was negative, then we'd have a percent decrease.

The formula shown above for C is basically having us compute the difference in price (B-A) and then we divide that difference over the original price A. This computes the decimal form of the answer. The "100*" tacked out front will convert from decimal to percent form.

If you took 52.94% of the original price 4.25, then you would get 0.5294*4.25 = 2.24995 which rounds to 2.25; this is the amount the price increases so we add this to 4.25 and we get 4.25+2.25 = 6.50 which is the new share price.

Answer:

4x+3−9x= 3-5x

5+3.2n−6−4.8n= -1.6n-1

2y−5(y−3)= -3y-15

−1/2(8b+3)+3b= -1b-1.5

Step-by-step explanation:

Add the numbers with the variables.

4x-9x= -5x

Then add the rest of the equation to it.

3-5x

Again, add the numbers with the variables and simplify the others.

3.2n- 4.8n= -1.6n

5-6= -1

That leads to....

-1.6n-1

Distribute the 5 into the parenthesis.

2y-5y- 15

Now, subtract the variables.

-3y-15

Distribute into the parenthesis.

-4b+(-1.5)+ 3b

Add the variables together.

-1b-1.5

Answer:

The consecutive even numbers are -42, -44, -46

Step-by-step explanation:

As the numbers are consecutive even integers,

Let,

The first number is "x"

The second number is "x+2"

The third number is "x+4"

According to the equation,

x + (x+2) + (x+4) = -132

As the sum is -132. Now we break the parenthesis by using the addition rule.

or, x + x + 2 + x + 4 = -132

or, 3x + 6 = -132

or, 3x = -132 - 6 (side change)

or, 3x = -138

or, x = -138/3 (interchange)

or, x = -46

Therefore, the first number is -46

The second number is -46+2 = -44

And the third number is -46+4 = -42

The consecutive even numbers are -42, -44, -46

Answer:

[tex]8\div9\times3\div16+1\div12=\frac{1}{4}[/tex]

Step-by-step explanation:

Given operation:

[tex]8\div9\times3\div16+1\div12[/tex]

Using PEDMAS to evaluate the order of operations.

First division:

[tex]=\frac{8}{9}\times\frac{3}{16}+\frac{1}{12}[/tex]

Next multiplication:

[tex]=\frac{1}{6}+\frac{1}{12}[/tex]

Then addition:

taking LCD of [tex]6\ and\ 12=12[/tex]

[tex]=\frac{2}{12}+\frac{1}{12}[/tex]

[tex]=\frac{3}{12}[/tex]

reducing to simplest fraction by division of both numbers by GCF.

[tex]=\frac{3\div3}{12\div3}=\frac{1}{4}[/tex]

Answer:

Step-by-step explanation:

The expanded form of the number 234.567 written using exponential notation  would be ...

  2×10² +3×10¹ +4×10⁰ +5×10⁻¹ +6×10⁻² +7×10⁻³

Note that exponents decrease going left to right (or increase going right to left). The exponent associated with the "ones" place is 0.

Apparently, you're supposed to write the negative powers as fractions, so you would have ...

  6.19 = 6×10^0 + 1×(1/10^1) + 9×(1/10^2)

1 An integer is a number that has no fractional part, and no digists after the decimal point. An integer can be positive, negative or zero. example 12, 34,-4,0 etc.

2. A natural number is a number that occurs commonly and obviously in nature. As such it is a whole, non -negative number. The set of natural numbers, denoted N, can be defined in either of two ways : N = (0,1,2,3,.......)

Natural numbers include 1, 2, 3, 4...; they are numbers you normally count and will go onto infinity and beyond. ZERO IS NOT A NATURAL NUMBER BECAUSE IT IS NEUTRAL.

Integers are all negative and positive counterparted whole numbers; e.g.... −4, −3, −2, −1, 0, 1, 2, 3, 4,...

I am joyous to assist you anytime.

Answer:

[tex]\displaystyle 79°[/tex]

Step-by-step explanation:

The m∠x is 79°, according to the Alternate Exterior Angles Theorem.

I am joyous to assist you anytime.

* That does NOT look like an acute angle because 79° is considered an acute angle, since it is less than 90°.

Answer:

126

Step-by-step explanation:

621 - x = 495

Subtract 621 from both sides.

-x = -126

Divide by -1

x = 126

Answer:

169/100

Step-by-step explanation:

93 + 76/100 = 169/100

Answer: 169/100

Step-by-step explanation:

The value of k will be 3 if the function is transformed by compression factor of 3

Step-by-step explanation:

The horizontal stretch or compression for a function f(x) is given by  g = f(bx) where b is a constant. If b> 0 then the graph of function is compressed.

As it is given in the question that he function is transformed by a compression factor of 3.

Given function

[tex]f(x) = 7^x+1\\To\ transform\\g = f(bx)\\g = 7^{3x}+1[/tex]

The value of k will be 3 if the function is transformed by compression factor of 3

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Answer:

11/15

Step-by-step explanation:

To answer this, add (combine) 1/3 and 2/5.

First we must rewrite these fractions with the same denominator, the LCD.

The LCD here is obtained by multiplying the denominators 3 and 5 together, obtaining 15.

Thus, 1/3 + 2/5 becomes 5/15 + 6/15, which, in turn, is 11/15.

The fraction of the total inventory that is children’s or women’s clothing

is 11/15.

Final answer:

To find the previous year's total revenue, divide the current year's revenue by 1.34 since the current revenue is 34% higher than the previous year. The calculation shows that the previous year's revenue was $25,000.

Explanation:

The question asks us to find the total revenue of a small business for the previous year, given that the current year's revenue is 34% higher. To do this, we let x represent the revenue from the previous year. Since this year's revenue is 34% more than last year's, we have the equation:

1.34x = 33,500

To find the value of x, we divide both sides of the equation by 1.34:

x = 33,500 / 1.34

x = 25,000

Therefore, the total revenue for the previous year was $25,000.