how many solutions are there for linear equations? what are they and how can you tell?

Answer:

The radian :

\( \frac{2\pi}{3} \)

The current weight of the truck is given as follows:

3496 kg.

The current weight of the truck is obtained applying the proportions in the context of the problem.

The initial weight of the truck is given as follows:

3796 kg.

The weight removed from the truck is given as follows:

6 x 50 = 300 kg.

Hence the current weight of the truck is given as follows:

3796 - 300 = 3496 kg.

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Answer:

Hi

Step-by-step explanation:

Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.

A scalene triangle can be identified by the inequality of the lengths of its sides and size of its angles.

The statements that complete the function transformations are left, up, stretch and stretch

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

f(x) = (x + 94)²

Also, we have

f(x) = x²

This implies that f(x) = (x + 94)² is obtained by shifting f(x) = x² left by 94 units

Next, we have

f(x) = x² + 94

This implies that f(x) = x² + 94² is obtained by shifting f(x) = x² up by 94 units

Next, we have

f(x) = 94√x from f(x) = √x

This implies that f(x) = 94√x can be obtained from vertically stretching f(x) = √x by a factor of 94

Also, the graph of f(x) = √94x can be obtained from horizontally stretching f(x) = √x by a factor of 1/94

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If z = (6x + 2y)⁹, then the partial derivatives of z are

• with respect to x :

∂z/∂x = 9 (6x + 2y)⁹⁻¹ • ∂(6x + 2y)/∂x

∂z/∂x = 9 (6x + 2y)⁸ • 6

∂z/∂x = 54 (6x + 2y)⁸

• with respect to y :

∂z/∂y = 9 (6x + 2y)⁹⁻¹ • ∂(6x + 2y)/∂y

∂z/∂y = 9 (6x + 2y)⁸ • 2

∂z/∂y = 18 (6x + 2y)⁸

Answer:

a. 2/25 =135/x

Hope it helps  :)

Step-by-step explanation:

Answer:

sounds like you're doing a geometry proof. First ask yourself if you believe BC=DA... then ask yourself why do you believe or know it to be true. keep challenging yourself until you find the reason.

Answer:

Step-by-step explanation:

180-90=2b+b

90=3b

90/3=b

30=b

2b=2*30

   =60

180-90=a+a

90=2a

a=90/2

a=45

the answer is 45 degrees

hope it helps!!let me know if it does

Answer:

a= 15°

Step-by-step explanation:

> use the fact that the sum of angles in a triangle is 180°

> based on the picture in the small right triangle we have b° +2b° +90° =180°

b +2b +90 =180° , combine like terms

3b +90 = 180, subtract 90 from both sides of the equation

3b = 90, divide by 3 both sides of the equation

b = 30°

> angle b has a ray that continues as a line so it makes an 180° angle and we have the acute triangle so we can write that

a + a+ (180-b) =180, substitute b

2a + 180-30 =180, subtract 180 from both sides, and add 30 to both sides

2a=30, divide by 2 both sides

a= 15°

The amount of direct materials cost in the unfinished job would be $97600.

The price of direct materials is directly related to the unit of production and is immediately identifiable. For instance, the price of glass is a direct material expense in the production of light bulbs. The primary component needed for the production of commodities or products was material. Costs of raw materials or components used directly in the production of goods are referred to as direct material costs. For instance, if Company A manufactures toys, the cost of the plastic used to build the toys would be an example of a direct material cost.

Given Data

Work in Process inventory account was credited for $120,500.

charged with $9,600 of applied overhead cost.

Direct material cost = Work in progress - Overhead cost - Direct labor

Direct labor = 9600 ×\(\frac{100}{75}\)

Direct labor = 12800

Direct material cost =  120000 - 9600-12800

Direct material cost = 97600

The amount of direct materials cost in the unfinished job would be $97600.

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The dairy farmer should use 400 pounds of the 75% protein supplement and 800 pounds of the 30% protein ration to make 1200 pounds of a high-grade 45% protein ration.

To determine how many pounds of each protein supplement the dairy farmer should use, we can set up a system of equations based on the given information.

Let's denote the following:

x = pounds of the 75% protein supplement

y = pounds of the 30% protein ration

The total weight of the mixture is 1200 pounds, so we have the equation:

x + y = 1200

The protein content in the mixture should be 45% of the total weight, so we have the equation:

0.75x + 0.30y = 0.45 * 1200

Now we can solve this system of equations.

First, let's rewrite the second equation in decimal form:

0.75x + 0.30y = 540

To make it easier to work with, we can eliminate the decimals by multiplying both sides of the equation by 100:

75x + 30y = 54000

Now we have a system of equations:

x + y = 1200

75x + 30y = 54000

We can solve this system using any appropriate method, such as substitution or elimination. In this case, let's use the substitution method:

Solve the first equation for x:

x = 1200 - y

Substitute the value of x into the second equation:

75(1200 - y) + 30y = 54000

Simplify and solve for y:

90000 - 75y + 30y = 54000

-45y = -36000

y = 800

Now we can substitute the value of y back into the first equation to find x:

x + 800 = 1200

x = 1200 - 800

x = 400

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Answer:

81.8 kg

Step-by-step explanation:

Answer:

81.8

Step-by-step explanation:

Decimals work just like basic addition.

Line it up at the decimal point.

  46.2

+ 35.6

_______

81.8

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer:

D=1

Step-by-step explanation:

1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1

Answer:

I honestly don't know but I think its all real numbers but not zero

Step-by-step explanation:

The train will cover 3.33 distance in one and a half hours.

What is the distance?

Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Here, we ave

Given: A train travels at an average speed of 100 kilometers per hour.

We have to find out If the train travel's for one and a half hour, what distance it covered.

Speed = 100kn

Distance=?

Time=   30 min

Distance = speed/time

Distance = 100/30

Distance = 3.33 meters

Hence, the train will cover 3.33 distance in one and a half hours.

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Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

1 inch = 3.5 feet

Step-by-step explanation:

Let's assume the desired answer is in the form 1 inch=x feet.  Then

16 inches=56 feet

1 inch=56/16 feet

1 inch = 3.5 feet

Answer:

9/10

Step-by-step explanation:

you can only add fractions when the denominator is the same, so u either have to multiply or divide a fraction. In this case, we'll multiply 4/5 with 10/10 so that the denominator will be the same as 5/50, and so that the value, 4/5(10/10), would still equal 4/5

4/5(10/10) + 5/50

40/50 + 5/50

45/50

simplify it

9/10

Answer:  A)  f(x) = (x-5)-8

Explanation:

To shift 5 units to the right, we replace x with x-5. This moves the xy axis 5 units to the left to give the illusion the function curve moves 5 units to the right. The -8 at the end shifts the curve down 8 units.

Answer:

0.26369

Step-by-step explanation:

Given that:

Mean precipitation (m) = 0.10 inches

Standard deviation (σ) = 0.07 inches

Probability that mean daily precipitation will be 0.107 inches (x) or more

x ≥ 0.107

Sample size (n) = 40

First find the Zscore

Using the relation :

Zscore = (x - m) / (σ / √n)

Zscore = (0.107 - 0.10) / (0.07 / √40)

Zscore = 0.007 / 0.0110679

Zscore = 0.632

Hence ,

P(Z > 0.632) = 0.26369 (Z probability calculator)

Answer:

A

Step-by-step explanation:

You know that you can simplify 6/9 because both the numerator (top number) and denominator (bottom number) can be divided by 3. Therefore, you divide them by 3 to get 2/3. 2/3 cannot be simplified anymore. 2/3 is equal to 2/3. Therefore, the answer is A.

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Answer:

a. the ratio is 1:2

b. its equivalent to the fraction 1/2

c. there would be 10 triangles

d. therw would be 45 triangles since the number of parallelograms is double the number of triangles

Answer:

See explanation.

Step-by-step explanation:

a) Simply divide the number of triangles by the number of paralellograms.

3/6

b) 3/6 is equal to 1/2.

1/2

c) Multiply 2 by 10 to get 20. Now, you also have to multiply 1 by 10.

10/20

d) There are three shapes for every instance of the ratio. Divide 90 by 3.

30

Hope this helped!

The expression given as -8+19+8 has a value of 19

From the question, the expression is given as

-8+19+8

Rewrite the expression properly

This is rewritten as follows

-8 + 19 + 8

Collect the like terms in the above expression

So, we have the following equation

-8 + 19 + 8 = 8 - 8 + 19

Evaluate the like terms in the above expression

So, we have the following equation

-8 + 19 + 8 = 0 + 19

Finally. we add 0 and 19

So, we have the following equation

-8 + 19 + 8 =  19

Hence, the valye of the expression is 19

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The obtained value of the given expression -8 + 19 + 8 would be 19 which is determined by using the arithmetic operation.

In mathematics, the addition, subtraction, division, and multiplication of built-in expressions can also be used to specify arithmetic operations.

The expression which is given in the question is below

⇒ -8 + 19 + 8

Rearrange similar terms in the above expression,

⇒ 8 - 8 + 19

Apply the subtraction operation,

⇒ 0 + 19

Apply the addition operation to get the answer,

⇒ 19

Hence, the obtained value of the given expression -8 + 19 + 8 would be 19 which is determined by using the arithmetic operation.

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(2x+4y=16).....1

(2x-4y=0).....2

then take equation 1 plus 2

4x=16

x=4

then take equation 2 to solve for y

2x-4y=0

(2×4)-4y=0

y=2

therefore answer is D. (4,2)

Answer:

?

Step-by-step explanation:

Problem 1

Sketch or describe the figure in Step 4 and Step 15.

Pattern of small squares. Step 1 has 1 square. Step 2 has 4 squares, 2 by 2 with bottom left square moved to top right corner. Step 3 has 9 squares, 3 by 3 with bottom left moved to top right corner.

How many small squares will there be in each of these steps?

Write an equation to represent the relationship between the step number, , and the number of small squares, , in each step.

Explain how your equation relates to the pattern.

Problem 2

Which expression represents the relationship between the step number  and the total number of small squares in the pattern?

A pattern of small squares. Step 1 has 0 squares. Step 3 has 3 squares: 2 by 2 but missing the lower right square. Step 3 has 8 squares: 3 by 3 but missing the lower right square.

A:

B:

C:

D:

Problem 3

Each figure is composed of large squares and small squares. The side length of the large square is . Write an expression for the area of the shaded part of each figure.

Figure A

Large square with 1 by 1 small squares removed from each corner.

Figure B

2 large squares side by side. On the side of the right square, there are 2 small squares stacked vertically, each with dimensions 2 by 2.

Problem 4

Here are a few pairs of positive numbers whose difference is 5.

Find the product of each pair of numbers. Then, plot some points to show the relationship between the first number and the product.

first

number second

number product

1 6  

2 7  

3 8  

5 10  

7 12  

Blank coordinate plane. Horizontal axis, first number, 0 to 10. Vertical axis, product, 0 to 100 by 10s.

Is the relationship between the first number and the product exponential? Explain how you know.

(From Algebra1, Unit 6, Lesson 1.)

Problem 5

Here are some lengths and widths of a rectangle whose perimeter is 20 meters.

Complete the table. What do you notice about the areas?

length

(meters) width

(meters) area

(square meters)

1 9  

3 7  

5    

7    

9    

Without calculating, predict whether the area of the rectangle will be greater or less than 25 square meters if the length is 5.25 meters.

On the coordinate plane, plot the points for length and area from your table.

Do the values change in a linear way? Do they change in an exponential way?

A blank graph, origin O, with a grid.

Problem 6

Here is a pattern of dots.

Four figures, labeled step 0 through 3. Step 0, row with 1 dot. Step 1, row with 2 dots. Step 2, row with 2 dots above row with 3 dots. Step 3, 2 rows of 3 dots above row with 4 dots.

Complete the table.

How many dots will there be in Step 10?

How many dots will there be in Step ?

step total number

of dots

0  

1  

2  

3  (From Algebra1, Unit 6, Lesson 2.)

Problem 7

Mai has a jar of quarters and dimes. She takes at least 10 coins out of the jar and has less than $2.00.

Write a system of inequalities that represents the number of quarters, , and the number of dimes, , that Mai could have.

Is it possible that Mai has each of the following combinations of coins? If so, explain or show how you know. If not, state which constraint—the amount of money or the number of coins—it does not meet.

3 quarters and 12 dimes

4 quarters and 10 dimes

2 quarters and 5 dimes

(From Algebra1, Unit 2, Lesson 25.)

Problem 8

A stadium can seat 63,026 people. For each game, the amount of money that the organization brings in through ticket sales is a function of the number of people, , in attendance.

If each ticket costs $30.00, find the domain and range of this function.

Answer:

The system of inequalities that can represent the situation is25q+0.1d<2.00 and  x+y≥10.

Yes, it is possible because 3 + 12≥10 and 3 quarters and 12 dimes total $1.95 which is less than $2.00.

This is not possible because 4 quarters and 10 dimes is exactly $2.00, which is not less than $2.00.

This is not possible because 2 quarters and 5 dimes is only 7 coins, which is not at least 10 coins.

Step-by-step explanation: