Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution, of allinfinite number of solutions. If the system has one solution, find the solution.4x + 2y = -2010x + 5y = -50

Answer:

c

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

you do change in y over change in x which is -7-9 over -1-3

when you do the calculations you get 4

Using the exponent's rule we know that x = 5.

Exponentiation is a mathematical process that involves the base b and the exponent or power n.

It is represented as bn and is pronounced as "b to the n."

A number's exponent indicates how many times to multiply that particular number.

It appears as a little number above and to the right of the basic number.

For instance, 82 = 8 x 8 = 64.

(The exponent "2" instructs us to multiply by two and use the number eight.)

Another illustration is 53 = 5 * 5 * 5 = 125.

So, we have: 2ˣ = 32

We know that:

2 * 2 * 2 * 2 * 2 = 32

2 is multiplied 5 times which means:

2⁵ = 32

Hence, x = 5.

Therefore, using exponents we know that x = 5.

Know more about exponents here:

https://brainly.com/question/19327364

#SPJ1

At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

For more such questions temperature,click on

https://brainly.com/question/25677592

#SPJ8

Answer:$31,500

Step-by-step explanation:

To calculate the total amount Mario will pay, including the loan amount and interest, for the loan from First Bank of Trust, we need to calculate the interest and add it to the loan amount.

The formula to calculate simple interest is:

Interest = (Loan Amount) x (Interest Rate) x (Loan Length)

Let's plug in the values given:

Loan Amount = $25,000

Interest Rate = 6.5% (or 0.065 as a decimal)

Loan Length = 4 years

Interest = $25,000 x 0.065 x 4 = $6,500

Now, let's calculate the total amount Mario will pay:

Total Amount = Loan Amount + Interest = $25,000 + $6,500 = $31,500

Therefore, the total amount Mario will pay, including the loan amount and interest, for the First Bank of Trust loan is $31,500.

The expression 48 − 8 × 48−8x48 is factored to give an equivalent expression 8(6 − x) × 48, where 8, 6, and x are terms of the expression. Factoring is the method of expressing a polynomial as the product of other polynomials. The term minus refers to subtraction, and the operation of subtraction is used to subtract 8 × 48 from 48 to get a result of 16.

The expression to factor is 48 − 8 × 48−8x48. Factoring the expression 48 − 8 × 48−8x48 gives an equivalent expression 8(6 − x) × 48, where 8, 6, and x are terms of the expression.

In mathematics, factoring is the method of expressing a polynomial as the product of other polynomials. The factored expression 8(6 − x) × 48 can be expanded back to the original expression by multiplying the individual factors with each other.

The term minus refers to subtraction. In this context, the operation of subtraction is used to subtract 8 × 48 from 48, yielding a result of 16. This result is multiplied by 48 − 8x48 to get the original expression 48 − 8 × 48−8x48.

Therefore, the equivalent expressions are 48 − 8 × 48−8x48 and 8(6 − x) × 48, where 8, 6, and x are terms of the expression.

For more questions on expression

https://brainly.com/question/1859113

#SPJ8

Answer:

382

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

Identify

2 × (2 - 6 + 3 + 64 × 3)

Step 2: Evaluate

Check the picture below, so Francesca's throw looks more or less like that, and it hits the ground when h(t) = 0

\(\stackrel{h}{0}=1+14t-5t^2\implies 5t^2-14t-1=0 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{5}t^2\stackrel{\stackrel{b}{\downarrow }}{-14}t\stackrel{\stackrel{c}{\downarrow }}{-1}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}\)

\(t= \cfrac{ - (-14) \pm \sqrt { (-14)^2 -4(5)(-1)}}{2(5)} \implies t = \cfrac{ 14 \pm \sqrt { 196 +20}}{ 10 } \\\\\\ t= \cfrac{ 14 \pm \sqrt { 216 }}{ 10 }\implies t=\cfrac{ 14 \pm 6\sqrt { 6 }}{ 10 }\implies t=\cfrac{ 7 \pm 3\sqrt { 6 }}{ 5 }\implies t\approx \begin{cases} ~~ 2.870~\checkmark\\ -0.070 \end{cases}\)

so there are two valid values, however we can't use the negative one, since the phenomena is for seconds and we can't have negative seconds in this case.

9514 1404 393

Answer:

  see below

Step-by-step explanation:

Each vertex has a single-letter label.

Each edge joins two vertices, and is named by naming those two vertices.

Each polygon is named by listing the vertices at its corners. It is a plane figure.

The base is the polygon opposite the point where all of the triangles come together.

__

16. figure: pentagonal pyramid ABCDEF

17. base: ABCDE

18. faces: ABF, BCF, CDF, DEF, AEF, ABCDE (the bottom face, or base)

19. edges: AB, BC, CD, DE, AE, FA, BF, CF, DF, EF

20. vertices: A, B, C, D, E, F

Answer:

10.8°degrees

Step-by-step explanation:

please click the heart and rate excellent and brainleist to ❤☺️☻♨️♨️☻☺️❤

Answer:

Step-by-step explanation:

There is 12 inches in a foot:  therefore, 12inches  x 7ft. = 84 ft.

Answer: 84 inches

Step-by-step explanation:

A conversion factor is a number that is used to multiply or divide one set of units into another.  For instance, 12 inches equals one foot when converting between inches and feet.

Since 1 foot = 12 inches

And we are trying to figure out how much inches are in 7 ft.

We can create a conversion (or cross multiply)

\(\frac{12}{1} =\frac{x}{7}\)

Where inches are in the numerator and ft are in demoninator.

When cross multiplying (multiplying in a diagonal) you get:

x = 84 inches

So 7 ft equals 84 inches.

---

A quicker method would be to multiply 7 ft by 12 inches/1 ft (foot), and get 84 inches.

--

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

For the first equation, we recall the commutative property of addition.

are equivalent.

For the second equation, we recall the commutative property of addition.

are equivalent.

For the third equation, we recall the commutative property of multiplication.

are equivalent.

Finally, for the last equation, we recall the commutative property of multiplication.

are equivalent.

Step1: Write out the expression

Step2: Write both notations to have the same exponent

Since the exponent are now having the same powers, take the common factor

The third option is correct

The range and IQR values of the Boxplot given are 12 and 5 respectively.

Range = 56 - 44 = 12

IQR = 53 - 48 = 5

Therefore, the range and IQR values are 12 and 5 respectively.

Learn more on Boxplot: https://brainly.com/question/30652189

#SPJ1

Answer:

2x(57x74)94

Step-by-step explanation:

Answer:

Step-by-step explanation:

n^3 + 512

512 = 8^3

So the factors are

(n + 8)(n^2 - nx + 64)

Answer:

try D(n+8) (n^2'8n+64)

Answer:

The point estimate for p is of 0.12.

The 90% confidence interval for p is 0.0862 < p < 0.1538.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

The manager of the dairy section of a large supermarket chose a random sample of 250 egg cartons and found that 30 cartons had at least one broken egg.

This means that \(n = 250, \pi = \frac{30}{250} = 0.12\)

The point estimate for p is of 0.12.

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a p-value of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 - 1.645\sqrt{\frac{0.12*0.88}{250}} = 0.0862\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.12 + 1.645\sqrt{\frac{0.12*0.88}{250}} = 0.1538\)

The 90% confidence interval for p is 0.0862 < p < 0.1538.

The factorized expression of 8^3 + 12x is 4(128+ 3x)

The expression is given as:

8^3 + 12x

Evaluate 8^3

8^3 + 12x = 512 + 12x

Factor out 2 from the expression

8^3 + 12x = 2(256+ 6x)

Factor out 2 from the expression

8^3 + 12x = 2 * 2(128+ 3x)

Evaluate the product

8^3 + 12x = 4(128+ 3x)

Hence, the factorized expression of 8^3 + 12x is 4(128+ 3x)

Read more about factorized expressions at

https://brainly.com/question/22048677

#SPJ1

Answer:

n is approximately 29 customers

Step-by-step explanation:

The given parameters are;

The mean duration of an order, μ = 4.5 minutes

The standard deviation, σ = 4

2 hours = 120 minutes

We get;

The z-score when the probability, P = 0.1 is P(z < 0.53983)

We have;

\(z = \dfrac{\dfrac{ \sum X_i}{n} - \mu_{\overline x}}{\dfrac{\sigma}{\sqrt{n} } }\)

Therefore, we get;

\(z = \dfrac{\dfrac{120}{n} - 4.5}{\dfrac{4}{\sqrt{n} } } = 0.53983\)

\(\dfrac{4}{\sqrt{n} } \times 0.53983 = \dfrac{120}{{n} } -4.5\)

With the aid of a graphing calculator, we get;

81·n²-4320·n + 57600 - 18.6506514278·n = 0

Factorizing gives;

(n - 24.3011921023)·(n - 29.2623961869)·81124141329 = 0

Therefore;

n ≈ 24 or n ≈ 29

Therefore, we take the largest number, n ≈ 29, to make the sample approximately normal

the correct option is D:

" The inverse relation must pass the vertical line test."

Remember that a relation is only a function if each value in the domain is only mapped into a single value in the range.

All functions need to pass what is called the "vertical line test" this means that if you draw a vertical line on the graph of the function, the vertical line can intersect the graph at most one time. If the vertical line intercepts the graph two or more times, then it is not a function.

From this we conclude that the correct option is D:

" The inverse relation must pass the vertical line test."

If you want to learn more about functions:

https://brainly.com/question/2328150

#SPJ1

The possible variable terms are a2b3, a5b3, ab8, a3b5, a7b, and a6b5. These terms all contain the same number of a's and b's as the original expression, (2a4b)8.

The expansion of (2a 4b)8 can be found by multiplying the a coefficients and b coefficients by 8. The a coefficients would increase by a factor of 8 and the b coefficients would increase by a factor of 8. This means that the possible variable terms for (2a 4b)8 are all those that have 8 a's and 8 b's. This includes a2b3, a5b3, ab8, a3b5, a7b, and a6b5. These terms all contain the same number of a's and b's as the original expression, (2a4b)8, but with the coefficients multiplied by 8. For example, the term a2b3 would be the result of multiplying 2a4b by 8, which results in 16a32b. This can be simplified to a2b3. Similarly, a5b3 would be the result of multiplying 2a4b by 8, which results in 16a32b. This can be simplified to a5b3.

Learn more about variable here

https://brainly.com/question/29583350

#SPJ4

Answer:

Step-by-step explanation:

1. j

2. k

3. L

4. Lj

5. kL

6. jk

Answer:

Proportional and they are all equal to 10.25

Step-by-step explanation:

20.50/2=10.25

30.75/3=10.25

41/4=10.25

51.25/5=10.25

61.5/6=10.25

They all match. they are proportional.

Answer:

1st {-6, -3, 0, 3, 6}

Step-by-step explanation:

range is the output that is "y", so the range is a set of {-6, -3, 0, 3, 6}

Answer:

proportional

Step-by-step explanation:

test = 100%

Answer: The correct answer is that it is proportional?