Select the correct answer. What is the equation of the directrix of the parabola given by the equation (y − 3)2 = 8(x − 5)? A. y = 3 B. x = 3 C. x = 5 D. y = -5

Answer:

Step-by-step explanation:

57

Answer: 25%

Step-by-step explanation:

A function is an equation with one solution to every value of x for the variable y. A input of a specific type is paired with exactly 1 output by a function.

Quantities and their modifications, equations and surrounding structures, locations of forms and forms themselves are all included in the field of mathematics. The term "function" describes the connection between a group of inputs, of which each has a corresponding output. A function is an association between inputs and outcomes in which each input results in a single, unique output. Functions are typically denoted by the letter f. (x). The input is just a variable x. There are four primary categories of functionality available. depending on the following elements: on.

Given:

A function is an equation with one solution to every value of x for the variable y.

Each argument of a specific type is paired with absolutely one output by a function. Typically, functions are named f(x) or g instead of y. (x). When x equals 2, as directed by f(2), we should choose the value of given function.

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Answer:

1. 3 -1

2. 6-3

3. 20-8 adding the smallest and the highest#

The area of the rectangle with a length of (x + 5) cm and width of (x + 2) cm is (x² + 7x + 10) cm²

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

A rectangle is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel. The area of a rectangle is the amount of space that it occupies. The area is calculated using:

Area = length * width

The rectangle shown has a length of (x + 5) cm and width of (x + 2) cm. Hence:

Area = length * width

Substituting:

Area = (x + 5)(x + 2)

Area = x² + 2x + 5x + 10

Area = (x² + 7x + 10) cm²

The area of the rectangle is (x² + 7x + 10) cm²

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Answer:

B

Step-by-step explanation:

after 0 it's 1 and 4 is after 5

1 year = 365 days

1 day => 6 diapers

1 year => 365 × 6 = 2190 diapers changed per year

The two lines L1 and L2 are parallel

For two lines to be parallel the slope must be equal, hence we calculate the slope of the two lines

The slope, m of the linear function L1 is calculated using the points (–2, 9) and (1, 3)

m = (y₀ - y₁) / (x₀ - x₁)

m = (9 - 3) / (-2 - 1)

m = (6) / (-3)

m = -2

The slope, m of the linear function L2 is calculated using the points (–4, 10) and (3, –4)

m = (y₀ - y₁) / (x₀ - x₁)

m = (10 + 4) / (-4 - 3)

m = (14) / (-7)

m = -2

The lines are parallel

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If one order is selected, the probability of getting an order that is not accurate is 0.236.

Probability is a measure of the likelihood of an event occurring. The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. Scientific probability is built on the basis of probability theory.

The calculation is;

P(Not accurate ) is equal to [n(Not accurate) + (Not accurate)- n] /Total

Thus, we have;

P(Not accurate) is calculated as follows:

(60 + 32 + 12 + 38 + 122 + 12 - 12)/(280 + 245 + 122 + 331 + 60 + 32 + 12 + 38).

P(Not accurate) = 264/1120

P(Not accurate ) = 0.236

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Answer:

a₄ = 0

Step-by-step explanation:

using the recursive rule [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 2 and a₁ = 6 , then

a₂ = a₁ - 2 = 6 - 2 = 4

a₃ = a₂ - 2 = 4 - 2 = 2

a₄ = a₃ - 2 = 2 - 2 = 0

Answer:

W

Step-by-step explanation:

Answer:

scalene acute as its all sides length are not equall and its all angle are less than 90 degrees

Answer:

  (0, -3)

Step-by-step explanation:

You want a point on the graph of 4x -y = 3.

It is often convenient to choose an intercept when looking for a point that will satisfy the equation. Here, it is convenient to set x=0 to obtain y=-3.

A solution ordered pair is (0, -3).

__

Additional comment

Here, it will be more convenient to choose a value for x. Choosing a value for y can result in fractions becoming involved for the values of x. We prefer to avoid that.

  y = 4x -3 . . . . . . y=-3 when x=0; y=1 when x=1, so (1, 1) is another solution

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The equation for the function shown in the graph is y = sin(x + π/2).

The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function.

Given a graph of a sine function,

which shows the amplitude of 1,

and value of x-intercept is π/2, when y is 0, x is π/2

the equation for sine is

y = a sin(bx)

where a is the amplitude = 1

b is π

y = sin(x),

but given x-intercept π/2,

so, y = sin(x + π/2)

Hence option A is correct.

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Answer:

y = 13x - 41

Step-by-step explanation:

Parallel lines always have the same slope since

[tex]m_{2}=m_{1}[/tex]

Thus, the slope of the second line is m = 13.

We can find the y-intercept of the line by plugging in the points for x and y, 13 for m, and solving for b:

[tex]-2=13(3)+b\\-2=39+b\\-41=b[/tex]

Answer:

the expression "square root of 1+3a/25" makes sense for all values of a that are greater than or equal to -8.333.

Step-by-step explanation:

The square root of a number is only defined for non-negative values of that number. Therefore, for the expression "square root of 1+3a/25" to make sense, the value inside the square root must be non-negative.

1+3a/25 >= 0

This inequality can be rearranged to get the values of a for which the expression makes sense.

3a/25 >= -1

3a >= -25

a >= -25*3/3

a >= -25/3

a >= -8.333

Therefore, the expression "square root of 1+3a/25" makes sense for all values of a that are greater than or equal to -8.333.

Answer:

Letter A

Step-by-step explanation:

The justification for step 3 in the solution process is the subtraction property of equality. This property states that if two numbers are subtracted from each other on both sides of an equation, the two sides remain equal. In this case, step 3 is subtracting -0.3a from both sides of the equation, which results in a = 8.3.

Answer: A

Step-by-step explanation:

The requried solution of the differential equation is given as y = x⁴/4 + c₁x²/2 + c₁².

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.

here,

Given the differential equation,

y' = 2 √y . x

y' = dy/dx so,

dy/dx = 2√y.x
dy/√y = 2x dx
[tex]y^{-1/2}dy = 2xdx\\\sqrt{y} /[1/2] = x^2 + c_1[/tex]
y = [1/2(x² + c₁)]²
y = x⁴/4 + c₁x²/2 + c₁²  

Thus, the requried solution of the differential equation is given as y = x⁴/4 + c₁x²/2 + c₁² .

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Answer:

1

Step-by-step explanation:

C•1/J

C•K/J

K=C×J

K=175

when J =15

then C is;

C=K/J

175/15

C=11.67

The hypothesis is "the stars are visible".

The conclusion is "it is night".

This is because a conditional follows the format of "if hypothesis, then conclusion". It shortens to "If P, then Q".

It's fairly clear that the original conditional is true. There are some extremely rare exceptions, but mostly stars are only visible at night.

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

The converse is "If it is night, then the stars are visible".

Reason: The original "If P, then Q" format flips to "If Q, then P" when forming the converse.

The converse is false. The fact that it is night does not automatically lead to the stars being visible. For example, storm clouds at night can obscure the stars.

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

The inverse is "If the stars aren't visible, then it is not night".

We negate both the hypothesis and conclusion. The format of the inverse is "If not P, then not Q".

Like the previous statement, the inverse is false. Why? Because the stars not being visible doesn't automatically mean it's not night. We could have storm clouds covering up the stars. Or perhaps the city has a lot of light pollution to drown out the stars.

The converse and inverse have the same truth value, as they are equivalent statements (just phrased slightly different ways).

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

The contrapositive is "If it's not night, then the stars aren't visible".

The original conditional "If P, then Q" leads to the contrapositive "If not Q, then not P". We swap the positions of P and Q. Also, we negate each piece. In a sense, we combine both the inverse and converse operations to get a contrapositive.

The contrapositive is true because "not night" of course means "day", in which the stars aren't present in the sky. The contrapositive and original conditional have the same truth value. The contrapositive is a way to rephrase the original conditional.

Answer:

Hypothesis:  "the stars are visible"

Conclusion:  "it is night"

Converse:  "If it is night, then the stars are visible" - false.

Inverse:  "If the stars are not visible, then it is not night." - false.

Contrapositive:  "If it is not night, then the stars are not visible" - true.

Step-by-step explanation:

Conditional statement

"If this happens, then that will happen."

Given conditional statement:

Therefore:

Converse statement

The converse of a conditional statement is formed by switching the hypothesis and the conclusion.

Therefore, the converse of the given conditional statement is:

This is a false statement as the stars will not be visible if there is cloud cover at night.

Inverse statement

The inverse of a conditional statement is formed by negating the hypothesis and the conclusion.

Therefore, the inverse of the given conditional statement is:

This is a false statement as the stars will not be visible if there is cloud cover at night.

Contrapositive statement

The contrapositive of a conditional statement is when both the hypothesis and conclusion are negated and then switched.

Therefore, the contrapositive of the given conditional statement is:

It is difficult to say if this is a true or false statement without more information, as it is possible to see bright stars during the daytime through a telescope or a really powerful pair of binoculars.

If we are to assume that "visible" means "visible to the eye" without any magnification assistance, then the statement is true (if we exclude the sun, which is a star).

Answer:

sight line & horizontal line

Step-by-step explanation:

varsitytutrs

The compound inequality for the graph given is  -2 < x < 5.

When a compound inequality is graphed such that there is an open circle instead of a filled - in circle over a number, then it means that x is either greater than this value, or less than this value. In other words, x is not equal to this value.

The circles over - 2 and 5 are not filled in which means that x is greater or less than - 2 and 5.

x is less than 5 because the arrow goes from 5 to infinity and x is greater than - 2 for the same reason.

The compound inequality is therefore:

-2 < x < 5

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The production of congruent figures involves stiff rigid transformation Even if you could imagine them as forms that "appear exactly the same," congruent figures.

During accurate modification of a geometric object, distance between each point pair is maintained. In other words, precise transformations maintain an object's size and shape. For instance, the angles and lengths of a triangle are preserved throughout a rigid transformation. Imagine a stiff shape, such as one made of cardboard, distorting. Even when the shape is rotated, mirrored, and moved left and right, nothing changes.

Here,

When I used putty to create a mold, it was the opposite. After that, users can stretch and twist the objects.

These ratios are not exact though. The distance between every pair of points is altered when the shape is stretched.

Applying rotations, reflection, and translations—three different forms of transformations—can result in congruent shapes.

In reality, by mixing any or all of these three transformations, any congruent shape pairs can be matched to one another.

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The complete question is " Do rigid transformations make congruent figures?"

Answer:

5625mm²

Step-by-step explanation:

The area of a square is found by multiplying the length of one side by itself. So if each tile is a square and measures 75mm on one side, then the area of one tile is:

75mm x 75mm = 5625mm²

The perimeter of polygon ABC = 67.4

The perimeter of polygon PQRS = 78.8

The perimeter of a polygon is calculated by adding the lengths of all sides of the polygon together.

The Two-Tangent Theorem states that if two tangents are drawn to a circle from the same external point, then the tangents are congruent (have the same length).

Perimeter of polygon ABC = AB + BC + AC

AB = 10.5 + (23.2 - 11.2) = 22.5 [based on the Two-Tangent Theorem]

BC = 23.2

AC = 10.5 + 11.2 = 21.7

Perimeter of polygon ABC = 22.5 + 23.2 + 21.7 = 67.4

Perimeter of polygon PQRS = PQ + QR + RS + PS

PQ = 25

PS = 21.8

QR = 13 + 4.6 = 17.6

RS = 4.6  + 9.8 = 14.4

Perimeter of polygon PQRS = 25 + 21.8 + 17.6 + 14.4 = 78.8

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Answer:

Step-by-step explanation:

a PERSON SHOULD SPEND AT LEAST 35 DOLLARS A WEEK ON COFFEE

When Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include

A. 27, 22, 17, 12, 7

D. 100, 95, 90, 85, 80

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, when Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include 27, 22, 17, 12, 7 and 100, 95, 90, 85, 80. In this cases, there are difference of 5.

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Complete question

Jackson wrote different patterns for the rule "subtract 5". Select all of the patterns that he could have written.

27, 22, 17, 12, 7

5, 10, 15, 20, 25

55, 50, 35, 30, 25

100, 95, 90, 85, 80

75, 65, 55, 45, 35

a) 5-5 is a numerical expression

b) c-5 is a variable expression where, variable is c

c) 8÷x+9 is a variable expression where, variable is x

d) 100·6 is a numerical expression

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Answer:

Step-by-step explanation:

The three numbers are 50, 40, and 27.

We can solve this equation by setting up a system of equations.

Let x be the first number, y be the second number, and z be the third number.

x + y + z = 117

y = x - 10

z = (1/2)x + 2

Substituting the equation for y into the first equation, we get:

x + (x - 10) + (1/2)x + 2 = 117

2x - 8 = 117

2x = 125

x = 62.5

Substituting this value of x into the other equations, we get:

y = x - 10 = 62.5 - 10 = 52

z = (1/2)x + 2 = (1/2)62.5 + 2 = 32.5 + 2 = 34.5

Rounding these values, the three numbers are 50, 40, and 27.

Answer:

Day 1: 8 pairs x $5.00/pair = $40.00

Day 2: 7 pairs x $5.00/pair = $35.00

Day 3: 15 pairs x $5.00/pair = $75.00

Day 4: 12 pairs x $5.00/pair = $60.00

Day 5: 31 pairs x $5.00/pair = $155.00

Day 6: 20 pairs x $5.00/pair = $100.00

Day 7: 35 pairs x $5.00/pair = $175.00

Total sales for the week: $40.00 + $35.00 + $75.00 + $60.00 + $155.00 + $100.00 + $175.00 = $605.00

Daily average of sales: $605.00 / 7 = $86.43

Total cost: 8 pairs + 7 pairs + 15 pairs + 12 pairs + 31 pairs + 20 pairs + 35 pairs = 128 pairs x $1.25/pair = $160.00

Profit: $605.00 - $160.00 = $445.00

So your total sales for the week were $605.00, your daily average of sales was $86.43, your total cost was $160.00 and your profit was $445.00