(06.03 HC)
Solve the following system of equations. Show all work and solutions.
y = 3x2 + 6x + 4
y = -3x2 + 4

a<-7 is the solution of the inequality. 8a < -56

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is 8a < -56

Eight times of a less than minus fifty six

8a < -56

Divide both sides by a

a<-56/8

a less than minus fifty six divided by eight

a<-7

Hence, a<-7 is the solution of the inequality. 8a < -56

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Answer:

[tex] \sf \: a < - 7[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of a.

The inequation is,

→ 8a < -56

Then the value of a will be,

[tex] \sf \rightarrow \: 8a < - 56[/tex]

[tex] \sf \rightarrow \: a < \frac{ - 56 \: }{ \: 8} [/tex]

[tex] \sf \rightarrow \boxed{ \sf a < - 7}[/tex]

Hence, the value of a is -7.

On solving the provided question, we can say that Principal = 21,000, interest = 0.4% and time = 4 yrs => SI = $336

Simple interest is calculated by dividing the principal by the interest rate, the passage of time, and other elements. The formula used in marketing is simple return = principal + interest + hours. Using this approach, interest may be calculated most easily. The most common way to calculate interest is as a percentage of the principal balance. If he borrows $100 from a friend and agrees to pay it back with 5% interest, for instance, he will only pay his proportion of the 100% interest. $100 (0.05) = $5. You must pay interest when you borrow money and charge interest when you lend it. The majority of the time, interest is calculated as an annual percentage of the loan balance. This proportion is referred to as the loan's interest rate.

here,

Principal = 21,000

interest = 0.4%

time = 4 yrs

SI = Principal X Interest X time / 100

SI = 21000*0.4*4/100 = $336

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When you are using the plane mirror, the image is going to have to be the same in size as you are.

When using the plane mirror and trying to get a reflection from the plane mirror, it would be found that the image that we are looking at in the mirror would turn out to be the same as the object that is being reflected. That is, your image is going to be exactly the same way.

The reason for this is because, the plane mirror is known to reflect light at the same angle that it received the light. This would cause the distance and the size of the object to be replicated in that image that has been reflected.

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Answer:

2 inches is longer than 5 cm.

Step-by-step explanation:

1 inch is exactly 2.54 cm. In this case, we should convert the inches to centimeters to have a better view of the problem. 2 inches times 2.54 equals 5.08 cm. 5.08 cm is longer than 5 cm. Therefore, the answer is 2 inches.

the answer is

2 in

2x2.54=5.08

5.08>5

1) The total number of possible outcomes is; 20 outcomes

2) The probability that someone  will adopt an adult cat that has grey fur is;  5%

In probability theory, conditional probability is defined as a measure of the probability of an event occurring, given the fact that another event has already occurred.

From the question;

Types of animals = 2 types

1) Dogs

2) Cats

Classification of Animals into age groups;

1) Babies

2) Adults

Colors of the fur of the animals;

1) Black

2) Brown

3) Tan

4) Grey

5) Mixed

1) The total number of possible outcomes = 2 * 2 * 5 = 20 outcomes

2) The probability that someone  will adopt an adult cat that has grey fur is; P(Adult cat and grey fur) = 0.5 * 0.5 * (1/5) = 0.05 = 5%

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Answer: Morgan will arrive at Town B at 5pm - 36 minutes = 4:24pm if she cycled at an average speed of 25km/h.

Step-by-step explanation: To solve this problem, we can use the formula: distance = speed x time.

We know that at 15km/h, Morgan reaches Town B at 6pm, and at 20km/h, she reaches Town B at 5pm.

We can use this information to find the distance between Town A and Town B and the time it takes to travel this distance at 25 km/h.

First, let's find the distance between Town A and Town B:

distance = speed x time

distance = 15 km/h x time

time = distance / 15 km/h

time = (distance / 15) hours

Since we know that when Morgan travel at 15km/h to reach town B at 6pm, we can use the time to calculate the distance:

time = 6pm - 5pm = 1hour

distance = 15 km/h x 1 hour = 15 km

Next, we can use this distance and the new speed 25km/h to calculate the arrival time:

time = distance / speed

time = 15 km / 25 km/h = 0.6 hours = 36 minutes

So, she will arrive at Town B at 5pm - 36 minutes = 4:24pm if she cycled at an average speed of 25km/h.

Please note that this calculation is assuming that the distance between Town A and Town B is a constant, and assuming that the time of arrival at 15km/h and 20km/h are accurate.

Answer: x = 10

Step-by-step explanation:

triangle shows angles are 38°, (7x+1)°, (10x+9)°(outside of the triangle)

total angle of the triangle is 180°

then

        38°+ (7x+1)°+ [180-(10x+9)°] = 180°

Simplifying

38 + (7x + 1) + [180 + -1(10x + 9)] = 180

Reorder the terms:

38 + (1 + 7x) + [180 + -1(10x + 9)] = 180

Remove parenthesis around (1 + 7x)

38 + 1 + 7x + [180 + -1(10x + 9)] = 180

Reorder the terms:

38 + 1 + 7x + [180 + -1(9 + 10x)] = 180

38 + 1 + 7x + [180 + (9 * -1 + 10x * -1)] = 180

38 + 1 + 7x + [180 + (-9 + -10x)] = 180

Combine like terms: 180 + -9 = 171

38 + 1 + 7x + [171 + -10x] = 180

Remove brackets around [171 + -10x]

38 + 1 + 7x + 171 + -10x = 180

Reorder the terms:

38 + 1 + 171 + 7x + -10x = 180

Combine like terms: 38 + 1 = 39

39 + 171 + 7x + -10x = 180

Combine like terms: 39 + 171 = 210

210 + 7x + -10x = 180

Combine like terms: 7x + -10x = -3x

210 + -3x = 180

Solving

210 + -3x = 180

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-210' to each side of the equation.

210 + -210 + -3x = 180 + -210

Combine like terms: 210 + -210 = 0

0 + -3x = 180 + -210

-3x = 180 + -210

Combine like terms: 180 + -210 = -30

-3x = -30

Divide each side by '-3'.

x = 10

Simplifying

x = 10

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The factors of x² - 9 is +3 , -3.

What is factors ?

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor in mathematics.

The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.

x² - 9 = 0

x² = 9

x = √9

x = ± 3

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Answer: To calculate how much the treats will cost, you need to multiply the cost per pound of the treats by the number of pounds Devyn wants to buy.

Cost = Price per pound x Number of pounds

Cost = 2.45 x 3.7

By performing this calculation we can get that the treats will cost : 2.45 x 3.7 = 9.095

So the treats will cost $9.095.

Step-by-step explanation:

Answer:

------------------------------------------------

Multiply the cost per pound by the amount of pounds:

From the equation y = 25x + 72, the initial temperature is 72°F, the rate of change in the oven temperature is 25 degrees Fahrenheit per minute

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let y represent the temperature of the oven in degrees Fahrenheit after x minutes.

Given the equation:

y = 25x + 72

This means that the rate of change is 25 degrees Fahrenheit per minute.

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The correct option is B, a vertical dilation by a factor of 3 and a horizontal shift to the right 2 units transformations are applied to the graph of the function f(x)=10^x to produce the graph of the function g(x)=3(10)^x-2.

An illustration of data or a mathematical function is a graph. Usually, it consists of a collection of plotted points or coordinates connected by lines or curves. A graph's main function is to show the relationship between two or more variables, which facilitates better comprehension and interpretation of the data.

The graph of the function f(x) = 10x is a three-fold vertical extension of the graph of y = 10x. In order to create the graph of g(x) = 3(10)x, a vertical dilation of three times is applied to the graph of y = 10x.

To create the function's graph, a horizontal shift of 2 units to the right is also used g(x) = 3(10)^x-2

So, the answer is B.

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Answer:

Below

Step-by-step explanation:

Circumference of circle = pi * d = pi * 2r

so:        circ / 2pi = r           56.52/(2 * 3.14) = r = 9 inches

AREA of a circle = pi * r^2

                           = 3.14 * 9^2 =   254.34 in^2

Answer: D the size of small tub

Step-by-step explanation: he needs to more if he is going to get his moneys worth

Donna need to know the size of small tub in order to decide which size is the better buy. the correct option is D.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that Donna could buy a half-gallon tub of ice cream for $4.99 or a small tub for $2.39.

We can see that he needs to more if he is going to get his moneys worth.

ice cream = $4.99

small tub = $2.39.

He need to know the size of small tub

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The domain is x < 2 or x ≥ 3 and the range y > - 3

The domain of a function is the interval of valid inputs to the function.

The range of a function is the interval of valid outputs to the function.

Since we have the function

To find the domain of the function, we see that the values of x are between x < 2 or x ≥ 3.

So, the domain is x < 2 or x ≥ 3.

To find the range of the function, since

f(x) = -x/2 - 2 if x < 2 and f(x) = 2x - 4 if x ≥ 3.

Using the first function f(x) = -x/2 - 2 if x < 2 and substituing x = 2, we have that

f(2) = -2/2 - 2 = - 1 - 2 = -3

Since f(x) cannot be less than f(2), then

f(x) > - 3

So, y > - 3

Also, using the second function f(x) = 2x - 4 if x ≥ 3. and substituting x = 3 into the equation since this is the minimum value of x, then

f(3) = 2(3) - 4

= 6 - 4

= 2

Since this is the minimum value of f(3) = 2

So, y > 2

Since y > -3 and y > 2, combining both expressions, we have that

y > - 3

So, the range is y < -3

So, the domain is x < 2 or x ≥ 3 and the range y > - 3

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Option A is the correct answer. An equation for a tangent to the graph of y=arcsiny/2 at the origin is x-2y = 0

The given equation is:

y=arcsiny/2---(1)

So to find the equation of the tangent line we required Fielding's first slope and we can find the slope by differentiating the equation of graft with respect to X.

The second thing we require is the point, also we have to find the slope accessible to zero

dy/dx=1/2/√1-x^/4

Also given that points meet at the origin means (0,0) the values of x, and y is 0 and substituted in the derivative equation, we get

y'(0)=1/2

y-0=1/2(x-0)

2y-0=x

x-2y=0

Therefore, An equation for a tangent to the graph of y = arcsin y/2 at the origin is x-2y=0

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The sum of the Polynomial as required to be used to verify the additive property is; 5x² + 5x +9.

Given polynomials p(x), q(x), and r(x), p(x) + ( q(x) + r(x) ) = ( p(x) + q(x) ) + r(x).

Hence, to justify the associative property; we must sum up the polynomials given in two ways as follows;

Method 1;

(3x + 4) + ( (5x² - 1) + (2x + 6) )

3x + 4 + ( 5x² + 2x + 5 )

3x + 4 + 5x² + 2x + 5.

Therefore, the sum is; 5x² + 5x + 9

Method 2;

(3x + 4) + ( (5x² - 1) + (2x + 6) )

= ( 3x + 4 + 5x² - 1 ) + ( ( 2x + 6 ) )

= 5x² + 3x + 3 + ( (2x + 6) )

5x² + 3x + 2x + 3 + 6

5x² + 5x +9

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On solving the provided question, we can say that we know that all angles of a parallelograms  are 360 => x = 23

A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two sets of parallel sides. In a particular kind of quadrilateral known as a parallelogram, both sets of opposite sides are parallel and equal. There are four different kinds of parallelograms, including three unique kinds. Parallelograms, squares, rectangles, and rhombuses are the four different shapes. Having two sets of parallel sides makes a quadrilateral a parallelogram. In a parallelogram, the opposing sides and angles are both the same length. On the same side of the horizontal line, the interior angles are additional angles as well. 360 degrees is the total number of interior angles.

as we know that all angles of a parallelograms  are 360

then, 3j +6k +(k+10) + (5j-9) = 360

3x + 6x + x +10 + 5x -9 = 360

15x = 349

x = 349/15

x = 23.2666666667 = 23

x = 23

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The solutions to this system are (x, y) = (1, 4), (x, y) = (0.5, 2), respectively.

Herein we find the case of a nonlinear system of the form f(x) = 0, which cannot be solved analytically. This solutions to this system by graphic approach, by means of algebra properties:

f(x) = 0

g(x) - h(x) = 0

g(x) = h(x)

By transitive property:

y = g(x)

y = h(x)

The solution to this system of the point of intersection of g(x) and h(x). The procedure is summarized below:

If we know that g(x) = 4 · x and h(x) = 4ˣ, then the solution to the nonlinear equations:

Points of intersection: (x, y) = (1, 4), (x, y) = (0.5, 2).

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Answer:

c is 80 and b is 100

Answer: C would be 80 degrees, and B would be 100 degrees

Hope this helps! :D

Answer:

78.54in2

Step-by-step explanation:

The standard form of a linear equation is Ax + By = C where A and B are not both zero and A, B and C are integers whose GCF is 1.

To convert the equation y = 9x - 1 to standard form, we need to rearrange it as:

9x - y = 1

We can divide both sides by -1 to get

-9x + y = -1

Which is the standard form of the equation.

So the standard form of the equation is:

-9x + y = -1

Answer: The y-intercept for part A is 2 and for part B is -5 and the slope for part A is 3 and for part B is 2. ✅

Step-by-step explanation:

PLEASEEEE GIVE BRANLIEST

The y-intercept is a point on the graph where the line of the function crosses the y-axis. It is represented by the number that is next to the y in the equation of a line (y = mx + b).

The slope is the steepness of the line and it is represented by the number that is next to the x (y = mx + b).

In part A, the y-intercept is 2 and the slope is 3. This means that the line starts at the point (0,2) and for every 1 unit on the x-axis, it goes up 3 units on the y-axis.

In part B, the y-intercept is -5 and the slope is 2. This means that the line starts at the point (0,-5) and for every 1 unit on the x-axis, it goes up 2 units on the y-axis.

So the difference between part A and part B is that the y-intercept for part A is 2 and for part B is -5 and the slope for part A is 3 and for part B is 2. This means that the line in part A starts at a different point and is steeper than the line in part B.

Answer:

In the context of a linear function, the y-intercept is the point where the line crosses the y-axis and the slope is the rate at which the line increases or decreases as the x-value increases. If two functions have different y-intercepts, it means that they have different starting points on the y-axis. Similarly, if two functions have different slopes, it means that they have a different rate of change. So, in part A and part B, if the y-intercept and the slope of the function in part A are different from the y-intercept and the slope of the function in part B, it means that the two functions have a different starting point on the y-axis and a different rate of change respectively.

Step-by-step explanation:

In the context of a linear function, a line can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b. For example, if the equation of the line is y = 2x + 3, the y-intercept is (0,3).

The slope of the line is the rate at which the line increases or decreases as the x-value increases. It is represented by the value of m in the equation y = mx + b. For example, if the equation of the line is y = 2x + 3, the slope is 2.

If the y-intercept and the slope of the function in part A are different from the y-intercept and the slope of the function in part B, it means that the two functions have different starting points on the y-axis and a different rate of change respectively.

For example, if the equation of the function in part A is y = 2x + 3, the y-intercept is (0,3) and the slope is 2. And if the equation of the function in part B is y = 4x + 1, the y-intercept is (0,1) and the slope is 4. Therefore, the y-intercept and slope of part A are different from the y-intercept and slope of part B.

The value of n of hours you need to study on Saturday is,

⇒ n = 3.75

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

The mean number of hours you study per day is 2.25.

Now, By definition of mean we get;

⇒ Mean = (2 + 1.75 + 2.5 + 2.75 + 3 + 0 + n) / 7

⇒ 2.25 = (12 + n) / 7

⇒ 2.25 × 7 = 12 + n

⇒ 15.75 = 12 + n

⇒ n = 15.75 - 12

⇒ n = 3.75

Thus, The value of n = 3.75

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The situation described is discrete data and the domain would be {x E Z | x >=0} where Z represents the set of integers and x is greater or equal to 0

What is the domain of a function?

The domain of a function is the set of all input values (also known as the independent variable) for which the function produces a valid output (also known as the dependent variable). In other words, it is the set of all input values for which the function is defined.

The situation described is discrete data.

The domain or set of all possible x-values for this situation would be the set of non-negative integers (x = 0, 1, 2, 3, ...) since the cost of each song is $3.00 and Clarissa can only buy a whole number of songs, not a fraction or decimal of a song.

Hence, the situation described is discrete data and the domain would be {x E Z | x >=0} where Z represents the set of integers and x is greater or equal to 0.

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The area issue with the suggested remedy is that the playing field is 118 feet by 56 yards in size.

To determine area, multiply length by width. L times B is the formula for calculating area. Area or Radius = r2(=3.14) These methods can also be used to calculate the areas of different quadrilaterals, which are polygonal shapes with four sides and an aspect lower than 90 degrees. Application. Since its inception, area has been the foundation of geometry.

Here,

Our calculation of w = 56 reveals that the parallelogram is 56 yards long.

We can simplify the calculation by altering w to 56 in order to obtain the length of the rectangle but since width is the same as 2w + 6 already.

The rectangle is depicted as having a length of 118 yards.

Accordingly, the playing field measures 118 yards by 56 yards.

Therefore, the size of the game field—118 yards x 56 yards—is the solution to the current problem.

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Answer:

t=-2

Step-by-step explanation:

5t-26=18t

5t-26+26=18t+26

simplify and subtract 18t from both sides

Therefore , the solution of the given problem of system of inequalities comes out to be option a.

This system of inequalities defines a region in the x-y plane. The first inequality represents all the points below a line with the equation y = 2 - x, and the second inequality represents all the points above a line with the equation y = x - 1. The solution to the system is the set of points that lie in the intersection of these two regions, which is a certain area of the x-y plane.

Here,

Given : This riddle can be represented by the following system of inequalities:

x + y < 2 (the sum of two numbers is less than 2)

x - y > 1 (if we subtract the second number from the first, the difference is greater than 1)

Where x and y are the two numbers.

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Due to the fact that parallel lines produce congruent alternate interior angles, ADB = CBD by ASA.

A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pains involve using freshly baked sorrowful bread. Prior to, before, ahead of The angles of 30 and 60 degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplementary angle is two angles combined to create a 180 degree angle. If the sum of two angles is 90 degrees, they are said to be complementary.

given

∠CDB = ∠ABD

and

∠ADB = ∠CBD

∠RQP = ∠SQP

since perpendicular lines form congruent right angles. PQ || PQ by reflexive so ∠PQR = ∠PQS by AAS.

Due to the fact that parallel lines produce congruent alternate interior angles, ADB = CBD by ASA.

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Answer: E⁢C=B⁢C; property of isosceles triangle

Step-by-step explanation: Got it right on Edmentum/Plato