Find the solution of the system of equations.
-9x + 2y = -19
5x + 4y = –15

Answer:

18m2

Step-by-step explanation:

Answer:

y=1.5

x=-3.5

Our answer is (-3.5,1.5)

Step-by-step explanation:

y-5=x

x=-2-y

y=?

--------

Using substitution,

y-5=-2-y

Solve:

2y-5=-2

2y=3

y=1.5

We can enter 1.5 into the equation:

1.5-5=x

-3.5=x

Answer: I believe

M = 80

Step-by-step explanation:

100 - 20 = 80

Answer:

C. There is a $2 fee to park, before the number of hours are factored in.

Step-by-step explanation:

Given that the equation, \( y = 3x + 2 \), represents total cost charged for at a parking lot for customers to park their car, thus:

the "x" represents the number of hours,

3 represents the charged fee per hour

2 represents the flat fee charged, which is the starting fee, before the number of hours is calculated and added.

Therefore, the answer is "C. There is a $2 fee to park, before the number of hours are factored in."

Answer:49

Step-by-step explanation:

A = \(\frac{3+11}{2}\) · 7

= \(\frac{14}{2} \\\) · 7

= 7·7

=49

Answer:

$280

Step-by-step explanation:

7•40=$280

Answer: Vegetable consumption per month is 17.33 pounds and fruits consumption per month is 10.47 pounds.

Step-by-step explanation:

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

1/6.

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.1666666 (6 repeating)  is 1/6

Answer:

Average rate of change=22

Step-by-step explanation:

We need to find the average rate of change of the equation: \(y=4x^2-10x+2\)between f(3) and f(5).

The formula used to find average rate of change is: \(Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}\)

In the given question we have a=3 and b =5

Finding f(a) i.e f(3)

\(f(3)=4(3)^2-10(3)+2\\f(3)=4(9)-30+2\\f(3)=36-30+2\\f(3)=8\)

Finding f(b0 i.e f(5)

\(f(5)=4(5)^2-10(5)+2\\f(5)=4(25)-50+2\\f(5)=100-50+2\\f(5)=52\)

Putting values of f(3)=8 and f(5)=52 to find average rate of change

\(Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}\\Average \ rate \ of \ change=\frac{52-8}{5-3}\\Average \ rate \ of \ change=\frac{44}{2}\\Average \ rate \ of \ change=22\)

So, Average rate of change=22

Answer:

A, C, E

Step-by-step explanation:

A. Nadiya is not correct. The inequality 8b+5≤36 describes how many batches she can make.

C. The solution to the inequality is b≤31/8

E. Since 5>31/8, 5 is not a solution.

Answer: A. -$157

Step-by-step explanation:

This is would be much more in debt for his credit card statement, it would take him longer to pay off.

Answer:

6,908.25$

Step-by-step explanation:

First, convert R to a decimal.

So R=0.1383

Next, 42 months = 3.5 years

A=4655(1+(0.1383 * 3.5))  = 6,908.25275

Answer:

16

Step-by-step explanation:

6+10 (TOTAL) is another word to compromise addition. So 6+10 = 16 cheonman- eyo

3 divided by sqrt8 + sqrt5=

3/(sqrt8+sqrt5)=

3(sqrt8-sqrt5)/(sqrt8+sqrt5)(sqrt8-sqrt5)=

(6sqrt2-3sqrt5)/3=

To find the polar equation of a conic with focus at the pole, directrix y=3, and eccentricity of 2, we can use the definition of a conic in polar coordinates.

The general form of the polar equation for a conic with focus at the pole is given by:

r = \(\frac{ed}{1+e\cos(\theta-\theta_0)}\)

Where:

- r is the distance from the origin (pole) to a point on the conic.

- e is the eccentricity.

- d is the distance from the pole to the directrix.

- θ is the angle between the polar axis and the line connecting the pole to a point on the conic.

- θ_0 is the angle between the polar axis and the line connecting the pole to the focus.

In this case, the focus is at the pole, so θ_0 = 0. The directrix is y = 3, which means its distance from the pole is d = 3. The eccentricity is given as 2, so e = 2.

Substituting these values into the general equation, we get:

r =\(\frac{2\cdot3}{1+2\cos(\theta-0)}\)

Simplifying further:

r =\(\frac{6}{1+2\cos(\theta)}\)

Therefore, the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2 is:

r =\(\frac{6}{1+2\cos(\theta)}.\)

This equation describes the shape of the conic in polar coordinates, where r represents the distance from the origin to a point on the conic, and θ represents the angle between the polar axis and the line connecting the origin to the point.

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A rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

To determine how many square tiles can fit in a rectangular floor, we need to calculate the total number of tiles that can fit both horizontally and vertically.

Given:

Length of the rectangular floor = 14 ft

Width of the rectangular floor = 6 ft

Edge length of square tile = 3/4 ft

First, let's calculate the number of tiles that can fit horizontally:

Length of the rectangular floor / Edge length of square tile = 14 ft / (3/4 ft) = 14 ft × (4/3 ft) = 56/3 ft

Since we want a whole number of tiles, we need to round down or take the floor value:

Number of tiles horizontally = floor(56/3) = 18 tiles

Next, let's calculate the number of tiles that can fit vertically:

Width of the rectangular floor / Edge length of square tile = 6 ft / (3/4 ft) = 6 ft × (4/3 ft) = 24/3 ft

Again, we round down or take the floor value:

Number of tiles vertically = floor(24/3) = 8 tiles

To find the total number of tiles, we multiply the number of tiles horizontally by the number of tiles vertically:

Total number of tiles = Number of tiles horizontally × Number of tiles vertically = 18 tiles × 8 tiles = 144 tiles

Therefore, in a rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

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Answer: 5 inspections in 4 hours, because if its 8 hours it would be 10 inspections

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

10 ÷ 8 = 1.25

The daily lunch sets cost $6, while the special lunch sets cost $36.

A linear equation with two variables consists of the greatest power of a variable being one.

Now, for the given condition in the question;

Let the price of the daily lunch set is 'x'.

Let the price of the special lunch set is 'y'.

Then, 2 daily lunch sets and 3 special lunch sets costs $120.

2x + 3y = 120     .......(equation 1)

And, 5 daily lunch sets and 2 special lunch sets costs $157.

5x + 2y = 157    ......(equation 2)

Using elimination method to solve equation 1 and 2.

y = 36 (price of each special lunch sets)

x = 6 (price of each daily lunch sets)

Therefore, the price for the daily lunch sets is $6 and price for special lunch sets is $36 in an restaurant.

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The expression shows the total amount in Diego's savings account after m months is 500 - 20m.

What is the total amount?

Two numbers are added together to form the sum. It is simple to figure out the sum of small integers. You can add two numbers using your fingertips. When two or more numbers are added together, a mathematical sum or maths sum is the outcome. It is the sum of the numbers when they are added up.

Here, we have

Given: Deigo has $500 in his saving account each month he takes out $20 to pay for karate class.

Let m be the number of months. Write an expression to show the total amount in Diego's savings account after m months.

The expression:

= 500 - 20m

Here m is the number of months

Hence, the expression shows the total amount in Diego's savings account after m months is 500 - 20m.

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1. The rate that Brand A is selling for is A) 10-unit rate.

2. The unit rate of Brand A is $0.10 per pound.

The unit rate refers to the variable cost per unit or the quotient of a division operation.

The unit rate shows a value's ratio in relation to another.

To compute the unit rate, we can use the division operation that makes the denominator the dividend, which is divided by the numerator (or divisor).

The quantity in Brand A = 20 pounds

The quantity in Brand B = 60 pounds

Cost of Brand A = $2

Cost of Brand B = $5

The unit rate for Brand A = $2/20 = $0.10, which can also be expressed as 10 units for $1 (20/$2).

Likewise, the unit rate for Brand B = $5/60 = $0.83, which we can describe as 12 units for $1 (60/$5).

Thus, we can conclude that the rate at which Brand A is selling is Option A.

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Answer Options:

A) 10-unit rate

B) 12-unit rate

C) 9-unit rate

D) 8-unit rate

ANSWER

1.015 L = 1,015 mL

EXPLANATION

To solve this we have to keep the relation 1 L = 1000mL in mind.

So if the soda bottle contains 2L, that is the same as 2000 mL. When we have to subtract two amounts (or add them) we always have to put them in the same units, so we either have to use them all in milliliters or in liters. Since the amount of soda they drank is less than 1000mL, it is better if we use milliliters:

The amount of soda left is 1015mL or, what is the same, 1.015 L

Jorge would earn $1,800 in interest over the course of one year.

We can determine the interest generated in a year if Jorge deposits $30,000 in an account that offers 6% yearly interest.

Interest = Principal * Rate

Principal = $30,000

Rate = 6% (which can be expressed as 0.06)

Interest = $30,000 * 0.06

Interest = $1,800

Therefore, Jorge would earn $1,800 in interest over the course of one year.

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The option that best describes the number of people who need glasses for reading by age 60 is d. most people

A condition known as age-related macular degeneration (AMD) affects a person's central vision. Although AMD can cause severe central vision loss, it rarely causes total blindness. Age 50 and older, smoking, having high blood pressure, and eating a diet high in saturated fat are all risk factors for AMD.

The 1960s and beyond are regarded as late adulthood. The process of physical change ends here. Skin elasticity continues to decline, as does reaction time and muscle strength. The senses of smell, taste, hearing, and vision that we had in our twenties start to deteriorate.

In this case, it should be noted that most people need glasses by 60 years and above. Therefore, the correct option is D.

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If the null hypothesis is correct, the probability that the test will result in a type 1 mistake is what is known as the alpha level for a hypothesis test. In other words, even in the absence of a treatment effect, the alpha level impacts the likelihood of collecting sample data in the critical zone.

The alpha level establishes the boundaries for identifying the key area that results in "extremely unlikely" or significant results that deviate from the null hypothesis. The likelihood of making a Type I error is one in twenty, according to researchers who use an alpha value or level of significance of.05.

The chance of rejecting the null hypothesis when it is true is known as the significance level, which is alternatively written as alpha or. For instance, a significance level of 0.05 represents a 5% probability of assuming the existence of a difference when none actually exists.

Hence we get the required answer.

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Answer:

Corresponding angles are congruent:

3x - 17 = 2x - 2, so x = 15.

Answer: Elijah would be 42 inches tall

Step-by-step explanation:

We all know that Samuel is 48 inches while Elijah is 6 inches shorter.

You subtract 6 from 48 to get 42.

Hopefully, this helped. :D