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When we divide fractions, we multiply the first fraction by the second fraction's reciprocal.

[tex]5\div \dfrac{7}{10}[/tex]

⇒ Multiply by the reciprocal of 7/10:

[tex]= 5\times \dfrac{10}{7}[/tex]

[tex]= \dfrac{50}{7}[/tex]

⇒ If you would like, you can change this into a mixed number fraction. The whole number value from 50/7 is 7. 7 times 7 is 49, which is 1 less than 50. 1 is the numerator and 7 is the whole number:

[tex]= 7\dfrac{1}{7}[/tex]

[tex]\dfrac{50}{7}[/tex] or [tex]7\dfrac{1}{7}[/tex]

The wire used for the triangular pendant can have a cost more than 664.65 USD and less than 791.25 USD.

In this problem we find the case of a triangle, in which the length of two sides are known and we need to determine the range of costs associated to the set of all possible triangles. This can be derived by the geometric system described in the image attached below. The minimum and the maximum costs of the pendant:

θ = 0°

l = 10.5 cm - 2.5 cm

l = 8 cm

s = 10.5 cm + 8 cm + 2.5 cm

s = 21 cm

C = (31.65 USD / cm) · (21 cm)

C = 664.65 USD

θ = 180°

l = 10.5 cm + 2.5 cm

l = 13 cm

s = 10.5 cm + 2.5 cm + 12.5 cm

s = 25 cm

C = (31.65 USD / cm) · (25 cm)

C = 791.25 USD

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The age of the paint is 14,290.0 years old

For any particular drug, understanding the concept of half-life is helpful in calculating steady-state concentrations and excretion rates. Although different drugs have different half-lives, they all adhere to the same principle: 50% of the initial drug dose is eliminated from the body after one half-life.

Since radiocarbon (14C) has a half-life of 5700 30 years, it is especially helpful for dating in archaeology. However, the so-called Gamow-Teller ß-decay, an exceptional hindrance to the beta decay from 14C to 14N, is what causes this half-life to be so long.

According to the given question :-

0.18 = e^(-0.00012t)

ln(0.18) = -0.00012t

t = - ln(0.18) / 0.00012 ≈ 14289.98690076605833 ≈ 14,290.0 years old

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Answer:

28:50

Step-by-step explanation:

22+28=50, and that is the total amount of students. The number of boys go first in the ratio, then total students.

Answer:

Mex$7,056

Step-by-step explanation:

$1 = Mex$20.16

$350 = x

cross multiply

$350 * Mex$20.60 = Mex$7,056

Answer: Mex$7056

Step-by-step explanation:

Make the proportion:

$1         -      Mex$20.16

$350    -          x

[tex]\displaystyle\\x=\frac{ 350(20.16)}{1} \\\\x=350(20.16)\\\\[/tex]

x=Mex$7056

Answer:

[tex]18x-9=18x-9\\\\3(6x-3)=18x-9\\\\x=4.5[/tex]

Step-by-step explanation:

Each equation is =72. So for the first 4 options, just find equivalent expressions for the left side:

[tex]\frac{3}{5}(30x-15)=18x-9\\\\18x-15\neq 18x-9\\\\50x-25\neq 18x-9\\\\18x-9=18x-9\\\\3(6x-3)=18x-9[/tex]

For x=4.5, must solve original equation:

18x-9 = 72

18x = 81

x = 4.5

The statements that are true for any value of x are

The equations are given as

A. 7x + (2x + 7) = 9x + 7

B. 7x + (2x - 1) = 9x + 1

C. 1/2x + (3 - 1/2x) = 3

D. 5x – (8 - 6x) = -x - 8

E. 0.4x - (0.2x + 8) = 0.2x - 8

F. 6x - (2x - 4) = 4x + 4

Next, we solve one side of the equations and then compare them with the other side

So, we have the following representations

A. 7x + (2x + 7) = 9x + 7

Evaluate

9x + 7 = 9x + 7 --- true

B. 7x + (2x - 1) = 9x + 1

Evaluate

9x - 1 = 9x + 1 --- false

C. 1/2x + (3 - 1/2x) = 3

Evaluate

3 = 3 --- true

D. 5x – (8 - 6x) = -x - 8

Evaluate

11x - 8 = -x - 8 --- false

E. 0.4x - (0.2x + 8) = 0.2x - 8

Evaluate

0.2x - 8 = 0.2x - 8 --- true

F. 6x - (2x - 4) = 4x + 4

Evaluate

4x + 4 = 4x + 4 -- true

Hence, the true statements are (a), (c), (e) and (f)

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The advantages and disadvantages of bases other than ten are shown below.

The base-10 system is a way to give numbers a place value. As the position of the decimal point determines a number's mathematical value, it is often referred to as the place value number system or the decimal system.

In software systems, number systems with a base of 16 are frequently used. They have the fundamental benefit of being quickly convertible to binary systems.

The advantage of using number bases on 60 is that 60 may be divided by 2, 3, 4, and 6.  Its downside is that it is cumbersome.

Number systems based on 12 provide advantages comparable to those of number systems based on 60, but they give up the advantage of being divisible by 5 for the benefit of a less cumbersome system.

Therefore, base-10 number systems are not the best.

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we get the desired result after solving as 4603.8 .

In mathematics, the BODMAS rule is a rule or order that is used to condense arithmetic expressions with several operators. When an equation has multiple operators, we must first determine the correct order in which to solve the expression. The BODMAS rule is always  used to resolve the issue of using algebraic symbols.

For this type of problem,

We generally use BODMAS

Here,

B= Bracket

O= Off

D= Divide

M= Multiply

A= Addition

S= Subtraction

Given expression,

3,000 + 1,600 + 8/10 + 3

By following above steps we get,

First we going to divide,

3,000 + 1,600 + 0.8 + 3

Then we move to addition,

4603.8

Hence we get the desired result as 4603.8

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The rocket reaches its maximum height at 2.25 second(s) after launch

The maximum height reached by the object is 88 feet.

Given function:

h(t) = -16t² + 72t + 7

By differentiating the function, we have

h'(t) = -32t + 72

Set the function to 0

-32t + 72 = 0

32t = 72

Divide both sides by 32

t = 2.25

Hence, the time is 2.25 seconds

To find the maximum height reached by the rocket,

Substitute t = 2.25 into

h(t) = -16t² + 72t + 7

h(2.25) = -16(2.25)² + 72(2.25) + 7

= -16(5.0625) + 162 + 7

= -81 + 162 + 7

h(2.25) = 88

In conclusion, the maximum height the rocket reached is 88 feet

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The value of x is 15 if the expression is  1/2x−5=10−3/4x after applying the arithmetic operation.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The expression is:

1/2x−5=10−3/4x

After solving:

5x/4 = 15

5x = 60

x = 60/5

x = 12

Thus, the value of x is 15 if the expression is  1/2x−5=10−3/4x after applying the arithmetic operation.

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The distance that Zoe rode while the car was behind her was of:

160 kilometers.

The relation between velocity, distance and time is that the velocity is the distance divided by time, hence the equation is presented as follows:

v = d/t.

The values of the parameters in this problem are given as follows:

(both of these measures are taken from the first sentence of the problem).

Then the total distance is obtained replacing the values into the equation as follows:

80 = d/4

d = 80 x 4

d = 320 kilometers.

The car was behind her for half the trip, hence the distance that the car spent behind her was of:

d = 0.5 x 320 = 160 kilometers.

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Answer: -4

Step-by-step explanation:

1. Add x on both sides

-8-x=x-4x → -8=2x-4x

2. Combine like terms

-8=2x-4x → -8=-2x

3. Divide negative 2 from both sides

-8=2x → -4=x

The solution for n in the chemistry formula is n = PV/RT

From the question, we have the following parameters that can be used in our computation:

Important formula from chemistry is PV = nRT

Write out the formula

So, we have the following representation

PV = nRT

Divide both sides of the equation by R

So, we have the following representation

PV/R = nT

Divide both sides of the equation by T

So, we have the following representation

PV/RT = n

Rewrite the equation as

n = PV/RT

Hence, the solution is n = PV/RT

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The evaluated expression of 24 / b + 8 when b = 9 is [tex]10\frac{2}{3}[/tex]

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) .

In other words, an expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it

To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations.

Therefore, let's evaluate 24 / b + 8 when b = 9

Hence,

[tex]\frac{24}{9}+8 = \frac{24+ 72}{9}=\frac{96}{9} = 10\frac{6}{9}=10\frac{2}{3}[/tex]

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a) If the sum of the square of the larger side is smaller than the squares of          the shorter sides, then the triangle is an acute triangle.

b) To determine if a triangle is a right triangle.

c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.

If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

Given,Pictures

According to the  converse of the Pythagorean Theorem.

a) If the sum of the square of the larger side is smaller than the squares of          the shorter sides, then the triangle is an acute triangle.

b) To determine if a triangle is a right triangle.

c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.

Therefore,

a) If the sum of the square of the larger side is smaller than the squares of          the shorter sides, then the triangle is an acute triangle.

b) To determine if a triangle is a right triangle.

c)If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.so, the second option is correct in the picture.

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Answer:

is there a photo because this dosent help

Step-by-step explanation:

Answer:

[tex]B. \;\dfrac{24}{40}[/tex]

[tex]C. \;\dfrac{3}{5}[/tex]

Step-by-step explanation:

The absolute value inequality to find the percentages is given as follows:

|P - 44| ≤ 3.

Then the percentages are given as follows:

The estimate of the percentage is of:

44%.

The margin of error is of:

±3%.

Both the estimate and the margin of error are taken from the problem.

This means that the absolute difference between the percentage P and the estimate of 44% is of at most the margin of error of 3%, hence the inequality is given as follows:

|P - 44| ≤ 3.

The absolute difference means that the difference can be either positive or negative.

Then the lowest percentage is obtained when:

P - 44 = -3

P = -3 + 44

P = 41.

The highest percentage is obtained when:

P - 44 = 3

P = 3 + 44

P = 47.

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The value of y when x = -3 represents that the population of the lizard three years before the researcher measures the population size is 63

From the question, we have the following parameters that can be used in our computation:

y = 500 * 2 ^ x

The above equation is an exponential function

Such that

x is the number of years after a researcher measures the population size

When x = -3, we have the equation to be

y = 500 * 2^-3

Evaluate the product

y = 62.5

Approximate

y = 63

This means that the value of y at x = -3 is 63

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a. The monthly payment must be $193.53 in order to pay off the account at the end of 4 years.

b. The total interest paid will be $4372.02.

Figure 1 is representing a right-angle triangle and figure 2 is representing the isosceles triangle.

The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.

As per the given diagram in the question,

For figure 1.

It is a right-angle triangle because it contains an angle of 90°.

For figure 2.

It is an isosceles triangle because according to the figure its two sides are the same which indicates that it is an isosceles triangle.

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Answer:

x = 4

Step-by-step explanation:

to find the zero equate f(x) to zero , that is

5x - 20 = 0 ( add 20 to both sides )

5x = 20 ( divide both sides by 5 )

x = 4

then the zero is x = 4

Answer:

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

Let's simplify left sides of each statement and compare with right sides:

Answer:

It should be 42.4

Answer:

6 hours I think

The amount will be $6660 after 3 years. It can be solved by the cocept of the compound interest.

What is compound interest?

In compound interest, the interest is added in the principal amount after the end of each term. The value after addition the interest is considered as the principal amount for the next term.

The annual interest is 5.2% hence, monthaly interest will be 5.2\12%

Apply the formula of conpound interest.

[tex]A=P(1+\frac{r}{100})^t[/tex]

Here, A is the total amount after the end of time period t, P is the initial amount, and r is the rate of intrest at which the amount is compounded.

Substitute $5700 for P, 5.2/12% for r and 36 for t. Here t is 36 becasue the amount compounded monthly and there are 36 months in a year.

 [tex]A=\$ 5700(1+\frac{5.2/12}{100})^{36}\\= \$ 6660[/tex]

Hence, the amount will be $6660 after 3 years. It can be solved by the cocept of the compound interest.

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Answer:

= -0.4

Step-by-step explanation:

3d-4 when d=1.2

3(1.2) - 4

3.6 - 4

= -0.4

Answer: 0.4

Step-by-step explanation:

Equation: 3d - 4

1. Substitute the variable with the given number (d = 1.2)

3(1.2) - 4

2. Solve 3 × 1.2

3.6 - 4

3. Solve

3.6 - 4 = -0.4

Answer:

Negative slope of 3 so -3x and -9y

Step-by-step explanation:

-3x=-9y

Answer:

slope = -3 ; y- intercept = (0,-9)

Step-by-step explanation:

A (-3,0)

B(0,-9)

slope = (-9-0)/(0-(-3)

-9/3

-3

Answer: y = 4x

Step-by-step explanation: The number of devices a company can produce is a function of the number of hours spent making the devices. On average, 4 devices are produced each hour. If we let x represent the number of hours spent making the devices and y represent the number of devices produced, we can write an equation to describe this relationship as follows:

y = 4x

This equation states that the number of devices produced is equal to 4 times the number of hours spent making the devices. For example, if the company spends 10 hours making the devices, the number of devices produced will be 4 * 10 = 40.

Therefore, the equation y = 4x describes the number of devices produced by the company as a function of the number of hours spent making the devices.