5x=3125 how do i solve that

The given equation is (1/2)a + (2/3) b = 50

and b = 30

Substituting the given value of b is above the equation we get

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a+\left(\frac{2}{3}\right)\times30=50 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow \left(\frac{1}{2}\right)a+20=50 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow\left(\frac{1}{2}\right)a=50-20=30 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{\Rightarrow a = 30 \times 2 = 60 } \end{gathered}$}[/tex]

Therefore, a = 60 and b = 30 is a solution of the given equation.

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Answer:

Step-by-step explanation:

The key word "product" tells us to multiply.

And, you probably know, but "integer" just means "number".

The question is, essentially:
A × B = 162 where A is half of B.

As someone who was never gifted in math, my best suggestion for something like this is to grab a calculator and start dividing 162 by all the numbers below 10. You will know you've got your answer when the calculator gives you a number that is twice the number you divided by.

In this case, I divided 162 by 9 and got 18. Since 9 is half of 18, and multiplied they make 162, we know this is the correct answer.

Hope this helps

Answer:

x = 2

Step-by-step explanation:

To solve the equation, you need to set both functions equal to each other and simplify to find the value of "x".

f(x) = 2x + 1

g(x) = -x + 7

f(x) = g(x)                                              <----- Given equation

2x + 1 = -x + 7                                      <----- Insert functions

3x + 1 = 7                                             <----- Add "x" to both sides

3x = 6                                                  <----- Subtract 1 from both sides

x = 2                                                    <----- Divide both sides by 3

The systems of linear equations have been matched with their respective solutions as shown in the image attached below.

A system of linear equations can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).

In this exercise, you're required to match the systems of linear equations with their respective solutions as shown in the image attached below.

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As the value of x increases and the function of f(x) also increases since it is moving in the upward direction. The x-intercept is (-3,0)

A function is a set of input values into a program that produces the desired output. In mathematical terms, we can say a function is a set of x values that maps to a set of y values.

Functions can also be represented on the graph called graphical representation.

From the given graphical information, as the value of x increases, the function of f(x) also increases since it is moving in the upward direction.

The x-intercept is the value where the line cuts the horizontal x-axis when y is zero, therefore the x-intercept is (-3,0)

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The correct order of the numbers is 0.8 < 5/6 < 12/13. The correct option is B.) 0.8 < 5/6 < 12/13

From the question, we are to determine the correct order of the numbers

The given numbers are

5/6, 12/13, and 0.8

Convert the fractions to decimals

5/6 = 0.8333

12/13 = 0.923

Thus, the numbers are

0.8333, 0.923, and 0.8

Order the numbers from the smallest to the largest

0.8 < 0.8333 < 0.923

≡ 0.8 < 5/6 < 12/13

Hence, the correct order of the numbers is 0.8 < 5/6 < 12/13. The correct option is B.) 0.8 < 5/6 < 12/13

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The following integer values of x satisfy the given inequality,

4, 5, 6, 7, 8

What is an inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made using inequality.

Solving the Inequality

The given inequality is,

5x + 4 > 19

5x > 19 - 4

5x > 15

x > 15/5

x > 3

So, the required values of x must be greater than 3 in the given interval, [2,8]

Thus, the integer values of x in the the interval [2,8] that satisfy the given inequality are 4, 5, 6, 7 and 8 (∵ Square brackets of an interval denote inclusion of the terminal values).

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The slope intercept equation can be represented as follows:

y = 9 / 7 x + 1

y = 11 / 4 x - 8

y = 11 / 8 x + 6

The slope intercept equation can be represented as follows:

y = mx + b

where

Therefore,

The slope intercept equation can be represented as follows:

9x - 7y = - 7

7y = 9x + 7

y = 9 / 7 x + 1

11x - 4y = 32

4y = 11x - 32

y = 11 / 4 x - 8

11x - 8y = -48

8y = 11x + 48

y = 11 / 8 x + 6

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The rate at which she reads is 26 pages per hour

The given parameters are

Pages = 2 and 3/5

Time = 6 minutes

Convert the time from minutes to hour

Time = 6/60 hour

This gives

Time = 0.1 hour

The rate at which she reads is calculated as:

Rate = Page/Time

This gives

Rate = (2 and 3/5)/0.1 hour

Rewrite as:

Rate = 2.6 pages/0.1 hour

Divide

Rate = 26 pages per hour

Hence, the rate at which she reads is 26 pages per hour

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Answer:

502.4 ft²

Step-by-step explanation:

To find the individual area of the ring, you first need to find the area of the white circle. Then, you need to find the area of the circle and the ring (which can be found by adding the width of the ring to the radius of the circle). Finally, you can find the area of the ring through subtraction.

Area (White Circle)

radius = 1/2 diameter

radius = (1/2) x 36 ft

radius = 18 ft

Area = πr²

Area = π(18 ft)²

Area = π(324 ft²)

Area = 1017.36 ft²

Area (White Circle + Ring)

radius = 1/2 diameter + width of ring

radius = (1/2 x 36 ft) + 4 ft

radius = 22 ft

Area = πr²

Area = π(22 ft)²

Area = π(484 ft²)

Area = 1519.76 ft²

Area (Ring)

Area (Ring) = Area (White Circle + Ring) - Area (White Circle)

Area (Ring) = 1519.76 ft² - 1017.36 ft²

Area (Ring) = 502.4 ft²

Answer:

33600 m²

Step-by-step explanation:

The top and bottom horizontal sides are parallel, so this is a trapezoid with bases DC and AB. The height is BC.

area of trapezoid = (a + b)h/2

where a and b are the lengths of the bases, and h is the height.

We need to find the height, BC.

Drop a perpendicular from point A to segment DC. Call the point of intersection E. E is a point on segment DC.

DE + EC = DC

EC = AB = 360 m

DC = 600 m

DE + 360 m = 600 m

DE = 240 m

Use right triangle ADE to find AE. Then BC = AE.

DE² + AE² = AD²

DE² + 240² = 250²

DE² = 62500 - 57600

DE² = 4900

DE = √4900

DE = 70

BC = 70 = h

area = (a + b)h/2

area = (600 m + 360 m)(70 m)/2

area = 33600 m²

Answer:

33,600 m^2.

Step-by-step explanation:

This is a trapezium, so

Area = (h/2)(a + b)

=  (h/2) ( 360 + 600)

= 960h / 2

= 480h,

We find the value of h using Pythagoras:

250^2 = h^2  + (600-360)^2

h^2 =  250^2 - 240^2 = 4900

h = 70.

So the Area = 70 * 480

= 33,600 m^2

Answer:

x = 90°

Step-by-step explanation:

Hello!

The sum of angles on a straight line is 180°.

To find the value of angle x°, we can subtract all the given angles form 180°.

The value of x is 90°.

3 roada andy to billy

5 road billy to willies

3×5 =15 it's the answer 15

The rate at which Sean drank the slushy is 5 milliliters  per second.

The time it would take to drink all the slushy is 55 seconds.

In order to determine the speed at which the slushy was drank, divide the slushy drank in 13 seconds by 13 seconds.

Speed = slushy drank in 13 seconds / time

(275 - 210) / 13

65 / 13 = 5 milliliters  per second

Time it would take to drink all the slushy =total milliliters of the slushy / speed

275 / 5 = 55 seconds.

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The missing length in the right triangle as given in the task content is; 156.

It follows from the complete question that the triangle given is a right triangle and the missing length (longest side) can be evaluated by means of the Pythagoras theorem as follows;

x² = 144² + 60²

x² = 20736 + 3600

x² = 24,336

x = √24336

x = 156.

Remarks: The complete question involves a right triangle and the missing length is the longest side.

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Answer:

(0, -5)      (10/3, 0)

Step-by-step explanation:

First, convert the given equation into the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

3x - 2y = 10

2y = 3x - 10

y = 3/2x - 5

The y-intercept is -5.

Next, to find the x-intercept, let y = 0 and solve for x. X-intercept is the point where the graph intersects the x-axis, so the y-coordinate of x-intercepts are always 0.

3x - 2*0 = 10

3x - 0 = 10

3x = 10

x = 10/3

X-INTERCEPT

Plug y=0 into the equation and solve the resulting equation 3x=10 for x.

The x-intercept:

[tex]\left(\frac{10}{3},0\right)\approx \left(3.33333333333333,0\right)[/tex]

Y-INTERCEPT

Plug x=0 into the equation and solve the resulting equation −2y=10 for y.

The y-intercept:

[tex]\left(0, -5\right)[/tex]

Answer:

1.857 pounds

Step-by-step explanation:

If the clay is divided into 4 equal parts, we divide 7.5lbs by 4: 7.5/4 = 1.857 lbs

Answer:

3

Step-by-step explanation:

height = constant * width

let's rearrange this equation

constant = height/width

let's pick several  points as a proof

15/5 =3

6/2 =3

1.5/0.5 = 3

hope this helps you!!

Answer:

9/5

Step-by-step explanation:

First we have to find the constant k

m = k/(p-1)^2  (p-1)^ goes on the bottom of the fraction because of the inverse.

5 = k/(4-1)^2

5 = k/3^2

5 = k/9  Multiply both side by 9

45 = k  We know can use this constant to solve our problem

m = 45/(6-1)^2

m = 45/5^

m = 45/24

m = 9/5

The equation which represents the equation for the temperature, D , in terms of t is D(t)=5°cos{(π/3)t}+67°.

Given that the high temperature is 72 degrees and low temperature is 62 degrees at 3 A.M.

We know that temperature is the intensity of the heat present around us.

We know that,

Maximum temperature=72 degrees,

Minimum temperature=62 degrees, which occurs at t=3 hours

Now we can write the equation as:

D(t)=A cos(ct)+B

Where A, c, B are constants.

We have a minimum at t=3 a minimum means cos(ct)=-1

then we have that D(3)=A cos(c*3)+B

=A*(-1)+b

=35°

Here we solve that ,

Cos(c*3)=-1

this means that

c*3=-1

c*3=π

c=π/3

We also know that the maximum temperature is 72°, the maximum temperature is when cos(c*t)=1

D(t)=0=A(t)+B=72

With this we can find that values of A and b

-A+B=62

A+B=72

B=67

A=5

Equation will be D(t)=5 cos{(π/3)t}+67°.

Hence the equation for the temperature is D(t)=5 cos{(π/3)t}+67°..

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The probability that it willtake less than 34 minutes to complete the test is 0.1056

Given mean of 44 minutes and standard deviation of 8 minutes.

We have to find the probability that it will take less than 34 minutes to complete the test.

The probability lies between 0 and 1. The formula to calculate probability is number of items divided by total items but it can also be found through z test calculations.

We are using z test to find the probability.

Z=X-μ/σ

Where μ is sample mean and

σ= standard deviation

Z is z value

First we will find the p value from 34 to 44.

Z=34-44/8

=-10/8

=-1.25

P value for X<34=P(Z<-1.25)

=0.5-0.3944

=0.1056.

Hence the probability that it will take less than 34 minutes is 0.1056.

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Step-by-step explanation:

Chapter 3 of Wheels of Change .

But the bicycle craze had a more lasting impact on women’s clothing than just the use of bloomers. Thanks in large part to cycling, the innovation of rational dress reformers were starting to take effect by the end of the 1890s. Corsets were on their way out, dresses were getting shorter, and women no longer wore the heavy, bulky undergarments that gave them round, unnatural shapes. These changes went a long way toward unburdening women and setting the stage for them to be healthier and more active in the coming century.

Based on the excerpt, women in the 1890s became more independent and their lives improved as a result of

a rise in the popularity of bicycles.

a rise in the popularity of corsets.

cycling becoming less socially acceptable.

clothing becoming more restrictive.

Answer:

to promote safer, more comfortable styles of dress for women

Step-by-step explanation:

to promote safer, more comfortable styles of dress for women

the population of province is growing at the rate of 2.91%

the formula of the rate of growth of a population =

[(future population- initial population/initial population)*100]/time

population in 2016 = 4.2 milllion = 4200000

Population predicted in 20 years = 6.65 million = 6650000

so, initial population = 4200000

future population = 6650000

rate of growth = {(6650000- 4200000/4200000)*100]/20

                       = 58.33/20

                     = 2.91%

the population is growing at the rate of 2.91%

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Answer: 23/26

Step-by-step explanation:

Let’s say we have 3 spots, one for each of the three exchange students. It doesn’t matter who goes with who, we’re just going to choose people.

If LaQuinta is NOT one of the people chosen, then there are 25 possible people left to become tour guides. We will need to choose 3 of them, so there are (25 choose 3) = 2,300 ways.

With no restrictions, there are 26 people to choose from and 3 spots to fill. Therefore there are (26 choose 3) = 2,600 ways to fill these 3 spots with no restrictions.

The total probability is 2,300/2,600, which simplifies to 23/26.

It takes 4 weeks at minimum for each pair to hug at least once if they sit in random order.

Analyzing the Given Information

As per the given information,

Number of people = 8

It is given that they sit in random order every week.

W e assume that the order is not repeated.

There are 4 pairs and since a person hugs both the persons on his immediate left and right.

Determining the Number of Weeks

Total number of people to be hugged by each person = 7

Number of people hugged by a person in one week = 2

So, number of weeks taken by each to huge every other person = 7/2

⇒ It will take (3 +1) for every pair to hug.

It takes 4 weeks at a minimum for every pair to hug if we assume that  their order is not repeated.

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[tex]\large\bold\blue{ANSWER:-}[/tex]

Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.

Answer:

You subtract 249 minus 5

The situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

The given parameters are:

Initial = 5200

Rate = 5%

Because the population by 5% every year, then the situation is a geometric sequence.

The common ratio is then calculated as:

Ratio = 1 + Rate

This gives

Ratio = 1 + 5%

Evaluate

Ratio = 1.05

Hence, the situation represents a geometric sequence because the successive y-values have a common ratio of 1.05.

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Answer: 480

Step-by-step explanation:

20(12)(2) = 480