Question is shown above :

Answer: 3.2t − 2.4

Step-by-step explanation:

Add −3.6 and 1.2

Then, add −1.9t and 5.1t

3.2t − 2.4

The factored expression of 20 + 16 is 4 (5 + 4).

Factoring is the process of representing a given number or algebraic statement as the sum of its components.

A relevant strategy is used, depending on the situation, to identify the components.

Locating GCD (Greatest Common Divisor)

It is possible to factor an equation where every term has GCD 0 by eliminating GCD as a common component.

Employing Identity

The given expression is:

20 + 16

20 can be written as 4(5).

16 can be written as 4(4).

20 + 16 = 4(5) + 4(4)

Taking the common term out we have:

20 + 16 = 4 (5 + 4)

Hence, the factored expression of 20 + 16 is 4 (5 + 4).

Learn more about factors here:

brainly.com/question/29065045

#SPJ1

The value of the exponential equation is A = ( 8 ) x ^ -105/2

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

A = 8 / ( 7√x¹⁵ )   be equation (1)

On simplifying the equation , we get

The value of √x¹⁵ = x ^ 15/2

Now , the 7th root of √x¹⁵ is = x ^ 105/2

Now , the equation will be

A = ( 8 ) x ^ -105/2

Hence , the exponential equation is A = ( 8 ) x ^ -105/2

To learn more about exponents click :

https://brainly.com/question/28966438

#SPJ1

Answer:

[tex]9x^{2} +14x+1[/tex]

Step-by-step explanation:

We need to add these two polynomials together.

The simple way to do this is by adding like terms.

[tex]9x^{2}[/tex] stays the same as there is only one term.

However, we add the integer and the x term together.

So our final answer would be:

[tex]9x^{2} +14x+1[/tex]

A big number calculator is a software application or program designed to perform arithmetic operations on large numbers that cannot be easily handled by standard computer hardware and software.

Big numbers are typically defined as numbers that are too large to be stored in the registers or memory of a typical computer processor.

In a big number calculator, arithmetic operations such as addition, subtraction, multiplication, and division are performed using algorithms that are specifically designed to handle large numbers. These algorithms may use techniques such as long division, long multiplication, and other mathematical strategies to perform the required computations.

Big number calculators are often used in scientific and engineering applications where very large numbers are encountered. They can also be useful in cryptography, where large prime numbers are used for encryption and decryption operations.

Learn more about big number calculator here

brainly.com/question/25906713

#SPJ4

The option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we can see in the picture, we have given a function:

We have a function:

g(x) = 4log(x) + 4

To find x-intercept plug g(x) = 0

0 = 4logx + 4

x = 0.1

(0.1, 0)

The vertical asymptote:

x = 0

The range of a function:

(-∞, ∞)

Thus, the option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

The size is a 1/4-20 drill hole is 5.1mm

Many factors contribute to tap failure or breakage, but one fundamental and obvious factor is often overlooked. The problem is that this factor cannot be calculated accurately using traditional tap/drill charts.

There have been many changes since the tapping/drilling chart was first developed - programmable machines, rigid tapping, synchronous tapping, better tool holders, special tapping fluids, higher quality taps, etc.

Most importantly, the drill bits used to make the holes to cut have improved. Enhanced drill bit geometries, new chip flute geometries, coolant holes, improved HSS and carbide grades, and coatings such as TiN and TiCN greatly improve hole quality and size.

know more about drill hole click here;

//brainly.com/question/17953782

#SPJ4

The solution is, sin∅ = 12/13 & theta is placed on the second quadrant.

that means  the answer is C.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

Let's solve the equation for theta

cos∅=5/13

so, we get,

∅ ≈ 112.6

This means angle theta is placed on the second quadrant.

We use Pythagorean's Theorem to find the other leg to find the sine function.

13² = 5² + x²

so, we get,

x = 12

It's important to know that the sine function is equivalent to the ratio between the opposite leg and the hypothenuse, and it has to be positive because sine functions are positive when the angle is on the second quadrant.

sin∅ = 12/13

Hence, the answer is C.

To learn more on Pythagorean theorem click:

brainly.com/question/24302120

#SPJ1

Using the substitution to solve the following system of equations, 4x+2y=36

y=2x-2 we get value of x as 5 and y is equal to 8.

There are two methods for solving simultaneous linear equations: graphical methods and algebraic methods. The algebraic technique includes the substitution method as one of its categories.

We have two equations as,

4x+2y=36

y=2x-2

Substituting the value of y = 2x - 2 in the equation 1 we get,

4x + 2(2x - 2) = 36

4x + 4x - 4 = 36

8x = 36 + 4

8x = 40

x = 5

And y = 2 x 5 - 2 = 8

Therefore, the value of x is 5 and y is 8.

The algebraic approach for solving simultaneous linear equations is the substitution method. The value of one variable from one equation is substituted in the second equation, as the name implies. In this manner, a pair of linear equations is reduced into a single linear equation with only one variable, which can then be solved quickly. Before beginning to solve linear equations using the substitution approach, learn about the algebraic and graphical methods.

Learn more about substitution:

https://brainly.com/question/25869125

#SPJ4

Therefore , the solution of the given problem of linear equation comes out to be Emily used 8.1 pints of blue paint to paint her bedroom walls.

A straightforward regression curve is created using the equation y=mx+b. The y-intercept is m, and the slope is B. The previous line is usually referred to as a "math equation mixing numerous variables," even though y / y represent independent components. Only two variables are present in bivariate linear equations. There are no known solutions to application issues involving linear equations.

Here,

If 4/5 of the total paint used is white paint, then 1/5 of the total paint used is blue paint. We can use this information to find the amount of blue paint Emily used.

Let x be the total amount of paint used in pints. Then:

4/5 x = 8.1 (the amount of white paint used)

1/5 x = ?

To solve for the amount of blue paint, we can multiply both sides of the equation by 5:

1/5 x = ?

1/5 x * 5 = ? * 5

x = 40.5

So Emily used a total of 40.5 pints of paint. To find the amount of blue paint, we can multiply the total amount of paint by the fraction that represents the amount of blue paint:

1/5 * 40.5 = 8.1

Therefore, Emily used 8.1 pints of blue paint to paint her bedroom walls.

To know more about linear equation visit:

https://brainly.com/question/11897796

#SPJ1

The sum of squares formula is in statistics, one tool for assessing a dataset's dispersion is the sum of squares.

The term "sum of squares" refers to the total of the supplied integers' squares. It is the product of the squares of a dataset's variation. To do this, we must calculate the data's average and then square and add each data point's deviation from the mean. In algebra, the (a + b)2 identity is used to calculate the sum of the square of two numbers.

A formula can be used to determine the sum of the squares of the first n natural numbers. The mathematical induction concept can be used to get the formula. These fundamental arithmetic operations, which are necessary for algebra and statistics, are performed. The sum of squares of given numbers can be determined using a variety of methods.

Sum of squares = a2 + b2 = (a + b)2 - 2ab

Learn more about Sum of squares:

https://brainly.com/question/1808118

#SPJ4

The size of the state of Colima is 519,100 square metres.

Confusion results from the fact that 1 metre squared and 1 metre by 1 metre squared are the same. Yet, square metres and metres squared are fundamentally different in all other situations, therefore it is important to use care when referring to either one.

First, it is necessary to convert square kilometres into square metres.

100 hectómeters cuadrados make up one kilómetro cuadrado.

Hence, the state of Colima is as follows in square metres:

519,100 hectómetros cuadrados (5,191 kilómetros cuadrados x 100 hectómetros cuadrados/kilómetro cuadrado)

Hence, the size of the state of Colima is 519,100 square metres.

To know more about Square Metres visit:

https://brainly.com/question/22431243

SPJ1

Answer:

3%

Step-by-step explanation:

We know

In a shipment of 700 motors, 21 are defective.

Based on the shipment, what is the probability that a motor is defective?

We take

21 divided by 700, times 100 = 3%

So, the probability is 3%.

Jay's new balance if he made one transaction of $ 128, given the credit card balance is

To find the new balance, you first need to find the interest on the old balance by the formula :

= 3, 390.88 x 18. 6 % / 12 months per year

= $ 52. 56

Jay's new balance is :

= Old balance + Interest + New transaction

= 3, 390. 88 + 52. 56 + 128

= $ 3, 571. 44

The new credit card balance is $ 3, 571. 44.

Find out more on credit card balance at https://brainly.com/question/26867415

#SPJ1

Answer:

5

Step-by-step explanation:

There is a solution to the system of equations, and Brianna and Ahmed paid the same price for the items.

What is the system of equations?

A system of equations is a set of one or more equations that are to be solved simultaneously. The solution to a system of equations is the set of values for the variables that satisfy all the equations in the system.

In this case, the system of equations represents the amount that Brianna and Ahmed paid for 5 paintbrushes and 3 art canvases, and 10 paintbrushes and 6 art canvases, respectively. The system of equations is:

5x + 3y = 47 (Brianna's purchase)

10x + 6y = 94 (Ahmed's purchase)

To determine whether Brianna and Ahmed paid the same price for the items, we can compare the value of x and y that satisfy both equations. To do this, we can solve the system of equations using any method we prefer, such as elimination or substitution. Here, we'll use the method of substitution:

From the first equation, we can solve for y in terms of x:

5x + 3y = 47

3y = 47 - 5x

y = (47 - 5x)/3

Substituting this expression for y into the second equation, we get:

10x + 6y = 94

10x + 6((47 - 5x)/3) = 94

Simplifying, we get:

10x + 94 - 10x = 94

94 = 94

This equation is always true, regardless of the value of x.

Therefore, there is a solution to the system of equations, and Brianna and Ahmed paid the same price for the items.

To learn more about the system of equations, visit:

https://brainly.com/question/13729904

#SPJ1

Answer: 3.1 kg

Step-by-step explanation:

Total amount sold of apples and pears = 6.6 kg

Of that 6.6 kg, 3.5 kg is the weight of the apples.

Subtract the weight of the apples from the total weight of the apples and pears.

6.6 kg (total weight) - 3.5 kg (weight of apples) = 3.1 kg (weight of pears)

Ivan ran a total distance of 550 meters during football practice.

To calculate the total distance Ivan ran, we need to add up the distances he covered in each direction:

To find the total distance, we can add up the absolute values of each distance, since distance is a scalar quantity and is always positive:

Total distance = |300 m| + |(200 m)| + |50 m|

= 300 m + 200 m + 50 m

= 550 m

So Ivan ran a total distance of 550 meters during football practice.

Read more about distance

https://brainly.com/question/14335655

#SPJ1

The perimeter of the figure is 28 units

The perimeter of a figure is the total length of its boundary or outer edge. It is the sum of the lengths of all the sides of the figure. The perimeter is usually measured in units such as centimeters, meters, inches, or feet, depending on the measurement system being used.

The perimeter of this figure is the sum total length of the boundaries.

This can be calculated as;

P = 2 + 4 + 5 + 3 + 7 + 7

P = 28 units

Learn more on perimeter of figure here;

https://brainly.com/question/19819849

#SPJ1

Answer:

24

Step-by-step explanation:

Rect = 3*4 = 12

Rect 2 = 1*6 = 6

Triangle = (6-3)*1/2*4 = 6

6 + 6 + 12 = 24

The height of the​ heater is 5 feet.

The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs.

Given:

The length of one side of the base is 12 feet.

The slant height is 13 feet.

Using Pythagorean theorem we get

H² = slant height² - 1/2 base diagonal²

H² = 13² - 12²

H² = 169- 144

H² = 25

H= 5 feet

Learn more about Pythagorean theorem here:

https://brainly.com/question/14932148

#SPJ1

Answer:

The perimeter of the new space used for the playground is 108 feet.

The perimeter of the space used for the new playground is 150 feet.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

The current space is rectangular and has a length of 24 feet and a width of 26 feet.

and, the new space is 36 feet long.

let the width of new space is x.

Since, the two space are similar then the scale factor will be

= 36/24 = 1.5

So, the width of new space = 1.5 x 26 = 39 feet

Thus, the Perimeter of new space

= 2(l +w)

= 2 (36+ 39)

= 150 feet

Learn more about Scale Factor here:

https://brainly.com/question/30215119

#SPJ2

13×4=52

Ok Multiplacation is a simple Math formula everyone can do so you have to do this:

13+13+13+13=52

Now do this:

13×4=52

Answer is 52

With 95% confidence that the true population mean weight of the sardine cans is between 7.813 oz and 7.887 oz.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

here, we have,

In this scenario, we have a cannery that claims their sardine cans have a net weight of 8 oz. We want to test this claim by taking a simple random sample of 30 cans and measuring their weights

From our sample of 30 cans, we calculated a sample mean of 7.85 oz and a standard deviation of 0.1 oz. The sample mean is an estimate of the population mean, and the standard deviation tells us how much the weights in our sample vary from the mean.

To determine the cutoff values for the middle 95% of the mean weights in this distribution based on the sample data, we can use the t-distribution with n-1 degrees of freedom. The degrees of freedom in this case are 29, which is one less than the sample size.

Using a t-distribution table or calculator, we can find the t-value for a 95% confidence level with 29 degrees of freedom, which is approximately 2.045. We can use this t-value to calculate the margin of error for the sample mean as:

margin of error = t-value * (standard deviation / square root of sample size)

= 2.045 * (0.1 / √(30))

= 0.037

The margin of error tells us how much the sample mean is likely to vary from the true population mean. To find the cutoff values for the middle 95% of the mean weights, we add and subtract the margin of error from the sample mean as follows:

lower cutoff value = sample mean - margin of error

= 7.85 - 0.037

= 7.813

upper cutoff value = sample mean + margin of error

= 7.85 + 0.037

= 7.887

To know more about standard deviation here.

brainly.com/question/16555520

#SPJ1

9 inches is equal to 22.86 centimeter

To convert 1 inches to cm, we can use the following formula:

1 inch = 2.54 cm

The conversion factor is 2.54

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in cm = conversion factor × The length in inches

Substitute the values in the equation

9 inches = 9 × 2.54 cm

Multiply the numbers

= 22.86 cm ( rounded to two decimal places )

Therefore, 9 inch is 22.86 cm

Learn more about conversion factor here

brainly.com/question/23718955

#SPJ4

Forming linear equations, the cost of a t-shirt and a notebook will be $1 and $6 respectively.

What is a linear equation, exactly?

When the greatest power of a variable is 1, the equation is said to be linear. Another term for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There are three more constants in addition to the constant C: the variables x and y, the coefficients A and B, and the variables.

Now,

Given that

club A sold 2 t-shirts and 3 notebooks, and made $20.

Club B sold 2 t-shirts and 1 notebook, for a total of $8.

Let x and y be the cost of t-shirt and notebook respectively

then 2x+3y=20--->1

and 2x+y=8 --->2  will be the equations formed.

Now subtracting 2 from 1

we get 2x-2x+3y-y=20-8

2y=12

y=6

then  2x+6=8

x=1

Hence,

           the cost of a t-shirt and a notebook will be $1 and $6 respectively.

To know about linear equations visit the link

https://brainly.com/question/29739212

#SPJ1

This means that the given side lengths do not satisfy the converse of the triangle inequality theorem, and thus a triangle cannot be formed with side lengths 8, 9, and 17.

Given that they have three quadrants or more, triangles are considered polygons. It has a straightforward geometric shape. The letters ABC form a right-angled triangle when put together. Euclidean geometry creates a new rectangle of square when the borders are incompatible. Given that they have three sides and three corners, triangles are categorised as polygons.

Here,

No, it is not possible to form a triangle with side lengths 8, 9, and 17.

To see why, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Symbolically, for sides a, b, and c, this can be written as:

a + b > c

a + c > b

b + c > a

Let's check if these inequalities are satisfied for the sides of 8, 9, and 17:

8 + 9 > 17 (true)

8 + 17 > 9 (true)

9 + 17 > 8 (true)

All three inequalities are true, which means that the given side lengths satisfy the triangle inequality and a triangle can be formed.

In this case, we see that 8 + 9 = 17, which is exactly the length of the third side.

This means that the given side lengths do not satisfy the converse of the triangle inequality theorem, and thus a triangle cannot be formed with side lengths 8, 9, and 17.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer: The population three years ago was 156250.

Step-by-step explanation:

Let 3 years ago, the population of a city = P

Rate of growth (R) = 8% p.a.

Present population (P) = 1,96,830.

Therefore,

[tex]A=P(1+R100)n[/tex]

P = A÷(1 + 8/100)³

196830 ÷ (1+2/25)³

=156250.

3 years ago, the population of the city = 156250.

Answer:

a = √c²-b²

Step-by-step explanation:

Sup bro,

The correct answer is a = √c²-b²