j(x)=−45x+7; j(x)=−5

Answer:

(5,2)

Maximum

5

Step-by-step explanation:

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\texttt{\:Coordinates of vertex = (5,2)}\)

\(\texttt{The graph has a maximum} \)

\(\tt \: Axis\:\: of \:\; symmetry : x = 5\ \)

____________________________________

\( \large \tt Solution \: : \)

Coordinate of vertex is the point where there's a unique (only one) value of y for x :

\(\qquad \tt \rightarrow \: (5,2)\)

Since it's a downward parabola, it doesn't have defined minima, as it's value reach [ - infinity ]

and hence, it has a maximum, at the vertex.

Axis of symmetry is the line that divides the parabola into two equal regions that are mirror images of each other.

it is the line passing through vertex and parallel to y - axis.

\(\qquad \tt \rightarrow \: x = 5\)

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

A triangle with given sides (2, 2, 3), and (3, 5, 6) is an obtuse triangle and can be determined using the Pythagorean theorem.

Given :

The sides of the triangle are 6 cm, 10 cm and 12 cm.

To determine which three numbers represent the sides of an obtuse triangle, we can use the Pythagorean theorem. According to the Pythagorean theorem, the square of the third side equals the sum of the squares of the short sides of a right triangle. That is:

    (H)² = (P)² + (B)²

Obtuse Triangle:

An obtuse triangle is a triangle with one interior angle greater than 90 degrees. In an obtuse triangle, if one angle is greater than 90°, the sum of the other two angles is less than 90°.

Obtuse triangle condition:   (P)² + (B)² < (P)²

Applying the obtuse triangle condition in option a) ( 4,7,8) is more than 8² .This means 4²+ 7²= 65 < 64. So option A) represents not an obtuse triangle.

Apply obtuse triangle condition in option B) (3,4,5) :

3² + 4² = 25

This is the same. Therefore, option B) does not represent an obtuse triangle.

Option C) applies the obtuse triangle condition: (2,2,3)

therefore, 2² + 2² < 3²

This is less than 3². So option C) represents an obtuse triangle. Apply

Option D) obtuse triangle condition greater than

Option D) (6,8,9) represents: 6² + 8² > 9²

Therefore, option D) does not represent an obtuse triangle.

Applying the obtuse triangle condition in option E) (3,5,6)

Which represents: 3² + 5² < 6²

This is less than 6².                                      

Therefore, option E) represents an obtuse triangle.

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Answer:

Step-by-step explanation:

(-1 -4)/(2 - 3) = -5/-1 = 5

y - 4 = 5(x - 3)

y - 4 = 5x - 15

y = 5x - 11

To identify the slope and y-intercep of a line, you need to write the equation in slope intercpet form:

m is the slope

b is the y-intercept (the value of y when the line cross the y-axis)

To write the equation in slope-intercept form, leave the variable y in one side of the equation.

-Substract 7x in both sides of the equation:

-Divide both sides of the equation into 2:

#1

Centre(4,-2)

Radius=11

Equation

#2

On comaparing to equation of Circle

#3

Same like last one

Answer:

$4.56

Step-by-step explanation:

22.80/5 = 4.56

The statement is False. The expression evaluates to 2.0, not 2.5.

The expression (double) (10 / 4) involves several steps of evaluation. Let's break it down to understand the process.

Integer Division: The division operation 10 / 4 is performed first. In integer division, the result is the quotient of the division without any decimal places. In this case, 10 / 4 equals 2, as the fractional part is truncated.

Type Casting: The expression (double) is a type cast that converts the result of the division to a double data type. However, the type casting occurs after the integer division has already taken place. So, the result of the type casting will not affect the value obtained in the integer division.

As a result, the expression (double) (10 / 4) evaluates to 2.0, not 2.5. The value 2.0 is a double representation of the integer 2. The type casting only affects the data type of the value, not its actual numerical value.

Therefore, the statement "The following expression will evaluate to 2.5: (double) (10 / 4)" is false. The expression evaluates to 2.0.

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True. The expression (double) (10 / 4) will evaluate to 2.5.

To evaluate the given expression, we need to follow the order of operations. First, we have the casting operation, which involves converting the result of the division to a double data type. Then, we have the division operation, which involves dividing 10 by 4.

Let's break down the steps:

Therefore, the expression (double) (10 / 4) will evaluate to 2.5.

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Any value inside an absolute value in a problem or equation indicates that the value is always positive.

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Answer:

Is that you in your pfp?

Step-by-step explanation:

Answer:

A then D then C then F thats what I see

Step-by-step explanation:

Answer:

158962.5

Step-by-step explanation:

it is already round to the tenth ,but if you are talking about rounding to the neartest whole number is it 158963

sorry if i am wrong :) have a nice day

If you are dealt five cards from an ordinary deck of 52 playing cards, the number of ways can you get a full house is 3,744.

A full house is a hand that contains three of a kind and a pair. For example, three aces and two kings are a full house. To calculate the number of ways to get a full house, use the following formula:

1. First, choose the rank for the three of a kind. There are 13 choices because there are 13 different ranks in a standard deck of cards.

2. Second, choose which three of the four suits for the three of a kind. There are four options for each card, but we must divide by 3! (the number of ways to order three cards) to correct for overcounting. Therefore, there are 4C3 * (3!) ways to pick three cards from four (equal to 4 ways to choose the three of a kind).

3. Third, choose the rank for the pair. This leaves 12 ranks to choose from since two of the 13 have already been used for the three of a kind.

4. Fourth, choose two suits for the pair. The suits for the pair must be different from those used for the three of a kind. There are four options for the first card, three for the second card, but we must divide by 2! to correct for overcounting. There are a total of 4C2 * 2! ways to pick two cards from four (equal to 6 ways to choose the pair).

We multiply these numbers to get the total number of ways to get a full house:

13 × 4C3 × 3! × 12 × 4C2 × 2! = 13 × 4 × 6 × 12 × 6 = 3, 744

Therefore, there are 3,744 ways to get a full house from a standard deck of 52 playing cards.

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Answer:

4 dimes is 40% of a dollar.

1 nickel and 3 pennies is 8% of a dollar.

5 quarters and 1 dime is 135% of a dollar.

Step-by-step explanation:

Hope it helps!

The vertex is at (-2, -9).

From the equation:

y = x² + 4x - 5

Transpose the c-value to the left side of the equation:

y + 5 = x² + 4x

Complete the square of the expression on the right side of the equation to get a perfect square trinomial:

y + 5 = x² + 4x + 4 - 4

by adding and subtracting 4 to the right side of the equation to maintain its balance.

Add the numbers on the left and factor the trinomial on the right:

y + 9 = (x + 2)²

Transpose the number across to the right side to get the equation into the vertex form, y = a(z-h)² + k:

y = (x + 2)² - 9

Make sure the addition and subtraction signs are correct to give the proper vertex form.

Here, the vertex is at (-2, -9).

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Given:-

To find:-

Answer:-

1) Firstly we are told to transpose the c value to LHS .

With respect to standard form of a quadratic equation, \( ax^2+bx + c \) ,the value of c here will be -5 . So on transposing c to LHS , we have;

\(\implies y + 5 = x^2 + 4x\\\)

w) Next we are told to complete the square on the RHS of the equation. For that add and subtract 4 .

\(\implies y + 5 = x^2 + 4x + 4 - 4 \\\)

\(\implies y + 5 =\{ (x)^2 + 2.2.x + 2^2 \}- 4\\\)

The terms inside the curly brackets are in the form of \( a^2+2ab + b^2\) , which is the whole square of \( (a + b )\) . That is \( ( a + b)^2\) . So , we can rewrite it as ,

\(\implies y + 5 = (x +2)^2 - 4 \\\)

\(\implies y + 5 + 4 = (x+2)^2 \\\)

3) Next we have to add the number on the left and factor the trinomial on right as ,

\(\implies y + 9 = (x+2)^2 \\\)

4) Now we are told to transpose the number on the LHS to RHS and get the equation into vertex form which is \( y = a(z-h)^2+ k \) .

\(\implies\underline{\underline{ y = (x+2)^2 - 9}} \\\)

This is our required answer in vertex form. Also on comparing to the standard equation of vertex form, we have;

\(\implies vertex = ( -2,-9) \\\)

and we are done!

The length of a side and the perimeter of the rhombus will be 5 units, and 20 units, respectively.

Given that:

A rhombus has diagonals of 6 and 8.

The side length of the rhombus is calculated as,

⇒ √((6/2)² + (8/2)²)

⇒ √(9 + 16)

⇒ √25

⇒ 5 units

The perimeter of the rhombus is calculated as,

P = 4 a

P = 4 x 5

P = 20 units

The length of a side and the perimeter of the rhombus will be 5 units, and 20 units, respectively.

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We have found that B can be expressed in terms of A as B = (P*A)*P.

We are given that A = PBP^(-1) and we need to solve for B in terms of A. To do this, we'll follow these steps:

Step 1: Multiply both sides of the equation by P.
P*A = P*(PBP^(-1))

Step 2: Use the property of matrix multiplication (AB)C = A(BC) to rearrange the terms.
P*A = (PP)B(P^(-1))

Step 3: Since P is invertible, PP^(-1) = I (Identity matrix), so we can simplify the equation.
P*A = I*B*P^(-1)

Step 4: As the identity matrix (I) has no effect on the product when multiplied, we can further simplify the equation.
P*A = B*P^(-1)

Step 5: Multiply both sides of the equation by the inverse of P^(-1), which is P.
(P*A)*P = B*(P^(-1)*P)

Step 6: Use the property of matrix multiplication again to rearrange the terms.
(P*A)*P = B*(P^(-1)*P)

Step 7: As P^(-1)*P = I (Identity matrix), we can simplify the equation.
(P*A)*P = B*I

Step 8: Since the identity matrix (I) has no effect on the product when multiplied, we get the final equation for B.
B = (P*A)*P
So, we have found that B can be expressed in terms of A as B = (P*A)*P.

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Answer:

common ratio r = - 2

Step-by-step explanation:

the common ratio r is calculated as

r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-32}{16}\) = - 2

Answer:

-2

Check:

16*-2 is -32

-32 * -2 is 64

Answer:

Step-by-step explanation:

The loop will run an infinite number of times

Answer:

40.5

Step-by-step explanation:

The value of the x is 6.

According to the statement

we have to find the value of the x.

So, For this purpose, we know that the

Let's assume PQ represents a line segment in the x,y plane and the complete line can be expressed as y=3x+14

QR represents another line segment in the x,y plane and the complete line can be expressed as y= 7x-10

Since the two lines intersect at point Q(x,y) the x & y values of both lines must be equal at point Q.

Thus, For this the equation become

3x+14=7x-10.

Solving for x yields x = 6.

So, The value of the x is 6.

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Answer:

??>?>?>\

Step-by-step explanation:

Answer:

The first blank is 400, the second is 20.

Answer:

send the complete question . there are some missing signs .

The area of each polygon in this problem is given as follows:

a) 252 square units.

b) 65 square units.

For item a, we have a rectangle of dimensions 12 and 21, hence the area is the multiplication of the dimensions, as follows:

A = 12 x 21 = 252 square units.

For item b, we have a triangle with base 13 and height 10, hence the area is half the multiplication of the base by the height, as follows:

A = 0.5 x 13 x 10 = 65 square units.

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Answer:

Step-by-step explanation:

For a point to be a solution to a system of inequalities, the points must make the signs of the inequalities true.

For example, the points must give results like 2<3 or 0>-2, these are true solutions. If the points gives 1>2, then that point is not a solution.

The proof of trigonometric identity (sin(x) + tan(x))/sin(x) = 1 +secx is given below.

The given trigonometric identity is,

(sin(x) + tan(x))/sin(x).

We know that tan(x) = sin(x)/cos(x), so we can substitute that in:

sin(x)/ sin(x) + sin(x)/cos(x) / sin(x)

We can simplify the fraction in the numerator:

sin(x)/ sin(x) + sin(x)/sin(x)cos(x)

We know that sin(x)/sin(x) = 1, so we can simplify further:

1+ 1/cos(x)

We know that 1/cos(x) = sec(x), so we can substitute that in:

1 + sec(x).

Now we have the same expression as the right-hand side of the identity, so we have proven that:

sin(x) + tan(x)/sin(x) = 1 + sec(x)

Therefore, (sin(x) + tan(x))/sin(x) = 1 +secx.

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Answer:

m=5

Step-by-step explanation:

1. Convert the logarithm into exponential form using the fact that \(log_{a}\)(x)=b is equal to x=\(a^{b}\) so ... 4m-10=\(10^{1}\)

2. Any expression raised to the power of 1 equals itself so ... 4m-10=10

3. Move the constant to the right-hand side and change its sign so ... 4m=10+10

4. Add the numbers so ... 4m=20

5. Divide both sides of the equation by 4 so ... m=5, m>\(\frac{5}{2}\)

6. Check if the solution is in the defined range so ... m=5

Answer:

125 pounds = 2500 five pence

Answer:

Step-by-step explanation

£1.00=100p

The number of ways to select 9 players for the starting lineup from a team of 15 players  is 4862 ways.

The number of ways to select 9 players for the starting lineup from a team of 15 players can be calculated using the formula for combinations, which is given by:

C(n,k) = n! / (k! (n-k)!)

Where n is the total number of items, k is the number of items being selected, ! means factorial, and C(n,k) represents the number of combinations of k items from n.

Using this formula, the number of ways to select 9 players from a team of 15 players is:

C(15,9) = 15! / (9! (15-9)!) = 15! / (9! 6!) = 4,862

So, there are 4,862 ways to select 9 players for the starting lineup from a team of 15 players.

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Answer:

Not a function fails the vertical line test

Step-by-step explanation:

This is not a function.  The value of x = -1  goes to two different values of y

This would fail the vertical line test

Answer:

the first one

Step-by-step explanation:

use the vertical line test. the horizontal line would intersect at two points.

The options are analyzed as follows:

1: The overline 0.729 means:

This is a non- terminating recurring decimal hence it is rational.

2: The nuumber 0.0195347... is a non terminating and non recurring decimal hence it is irrational.

3. The number -12 is rational since it is an integer.

4.The number 4.565656... is a non terminating recurring decimal hence it is rational.

5. The number given by:

Since square root of 2 is irrational and 3 is rational the product is irrational.

Also the decimal is non terminating non recurring hence it is irratonal.

So the options 2 and 5 are irrational.