The product of two consecutive square number is 144

Every year there are 14 more ducks. The starting point would be 50 and the equation is:

d = 14*year+50

y = x^2 to  Green

y = –2(x – 2)^2 + 2  Blue

The correct answer is D.

Answer:

The correct option is D.

Step-by-step explanation:

The parent function is

[tex]y=x^2[/tex]

The transformed function is

[tex]y=-2(x-2)^2+2[/tex]              .... (1)

The translation is defined as

[tex]f(x)=k(x+a)^2+b[/tex]                .... (2)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (1) and (2) it is clear that

[tex]a=-2,b=2,k=-2[/tex]

It means,

a=-2<0 the graph shifts 2 units right.

b=2>0 the graph shifts 2 units up.

k=-2, the graph reflect across the x-axis and stretch by the factor 2.

The graph reflect across the x-axis, translate 2 units to the right, translate up 2 units, stretch by the factor 2. Therefore the correct option is D.

The price of the stock of PEV Corporation varies as shown. we have to determine the net charge. Net change is just how much it changed overall, so we will look for all the ups minus all the downs.  

Here, "went up" goes with a + sign, and "went down" goes with a - sign.

So, Net charge = [tex]\frac{1}{4} - \frac{1}{3}-\frac{3}{4} + \frac{7}{10}[/tex]

= [tex]\frac{1}{4}-\frac{3}{4}- \frac{1}{3} + \frac{7}{10}[/tex]

= [tex]-\frac{2}{4}- \frac{1}{3} + \frac{7}{10}[/tex]

= [tex]-\frac{1}{2}- \frac{1}{3} + \frac{7}{10}[/tex]

LCM of 2,3 and 10 is 30

= [tex]\frac{-15-10+21}{30}[/tex]

= [tex]\frac{-4}{30}[/tex]

= [tex]\frac{-2}{15}[/tex]

So, the net charge is [tex]\frac{-2}{15}[/tex]

$6 dollars because 11-8 = 3, 3x2 =6

He starts with $6.00

It says he spends 1/2 of his allowance on the movies. 6/2=3

He has $3. Then it says He gained $8.00 for washing the "family" car.

$6.00+$8.00

=$11

Answer=$6.00

Answer:

1668

Step-by-step explanation:

8(8)= 64

64+4=68

1,600+68= 1,668

729 = s^3

9^3 = s^3

s = 9 in.

Answer: Answer would be 23

Step-by-step explanation:

This is how you would graph your function.

Suppose that Carol has x 10p coins in her purse. Since she has three times as many 20p coins as 10p coins, then she has 3x 20p coins in her purse.

x coins of 10p value $0.10x and 3x coins of 20p value $0.60x.

In total this amount of money is $(0.10x+0.60x)=$0.70x that is exactly $4.20. Thus, you get the equation

0.70x=4.20.

Solve it:

[tex]x=\dfrac{4.20}{0.70}=6.[/tex]

Carol has 6 coins of 10p and 3·6=18 coins of 20p.

Answer:

I'm not sure how euros work but I'm almost certain there are 18 20p coins

Step-by-step explanation:

To determine the approximate number of workers hired during the seventh year based on the quadratic model, we need more information about the model and the values of a, b, and c.

To approximate the number of workers hired during the seventh year based on the quadratic model, we need more information about the model. Quadratic models are typically of the form y = ax^2 + bx + c, where x represents the time and y represents the number of workers hired. Without knowing the values of a, b, and c, we cannot determine the exact number of workers hired in the seventh year. However, if we have the values of a, b, and c, we can substitute x = 7 into the equation to find the approximate number of workers hired during the seventh year.

Hello,

Please, see the attached files.

Thanks.

[tex]x^4-625=(x^2-25)(x^2+25)=(x-5)(x+5)(x-5i)(x+5i)\\\\x^4+10x^2+25=(x^2+5)^2=((x-\sqrt5i)(x+\sqrt5i))^2=(x-\sqrt5i)^2(x+\sqrt5i)^2[/tex]

Answer:

1) [tex]x^4-625=(x+5i)(x-5i)(x+5)(x-5)[/tex]

2) [tex]x^4+10x^2+25=(x+\sqrt{5}i)^2(x-\sqrt5 i)^2[/tex]

Step-by-step explanation:

1) Given : Expression [tex]x^4-625[/tex]

To find : Factor the expression completely over the complex numbers ?

Solution :

We can re-write the expression as,

[tex]x^4-625=(x^2)^2-(25)^2[/tex]

Applying identity, [tex]a^2-b^2 = (a+b)(a-b)[/tex]

[tex]x^4-625=(x^2+25)(x^2-25)[/tex]

[tex]x^4-625=(x^2+25)(x^2-5^2)[/tex]

Again apply same identity,

[tex]x^4-625=(x^2+25)(x+5)(x-5) [/tex]

The factor of [tex]x^2+25=(x+5i)(x-5i)[/tex]

Factor form is [tex]x^4-625=(x+5i)(x-5i)(x+5)(x-5)[/tex]

2) Given : Expression [tex]x^4+10x^2+25[/tex]

To find : Factor the expression completely over the complex numbers ?

Solution :

Expression [tex]x^4+10x^2+25[/tex]

Let [tex]x^2=y[/tex]

[tex]y^2+10y+25[/tex]

To factor we equate it to zero.

[tex]y^2+10y+25=0[/tex]

Apply middle term split,

[tex]y^2+5y+5y+25=0[/tex]

[tex]y(y+5)+5(y+5)=0[/tex]

[tex](y+5)(y+5)=0[/tex]

Substitute back,

[tex](x^2+5)(x^2+5)=0[/tex]

[tex](x^2+5)^2=0[/tex]

[tex]x^2+5=0[/tex]

[tex]x^2=-5[/tex]

Taking root both side,

[tex]x=\sqrt{-5}[/tex]

[tex]x=\pm \sqrt{5}i[/tex]

So, The factors are [tex](x+\sqrt{5}i)(x-\sqrt5 i)[/tex]

Factor form is [tex]x^4+10x^2+25=(x+\sqrt{5}i)^2(x-\sqrt5 i)^2[/tex]

Hello,

To solve we need to factor y^2-2y-35:

(y-7)(y+5)=0

Now solve for :

(When will (y-7)(y+5)equal zero?)

When y-7=0 or y+5=0

Solve for the 2 equations above and;

y= 7,-5

Hope this helps, have a great day!

probability has 11 letters

2/11 chances that you could get a B

5/9 for a T or vowel

3/11 for an O or B

you just look at the letters and the number of them

Answer:

1)  a=12 , b=-9 , c=4

2)  a=-1 , b=-10 , c=2

3)  a=5 , b=-1 , c=9

4)  a=1 , b=-8 , c=16

Step-by-step explanation:

(1) y = 12x² - 9x + 4 no real solutions.

(2) 10x + y = -x² + 2, two real solutions.

(3) 4y - 7 = 5x² - x + 2 + 3y, no real solution.

(4) y = (-x + 4)², one real solution.

The number of real solutions for each quadratic equation is determined using discriminant.

The discriminant, denoted as Δ, is used to determine the nature of the roots of a quadratic equation of the form ax² + bx + c = 0.

Δ = b² - 4ac

From the given equations;

y = 12x² - 9x + 4

a = 12, b = -9, c = 4

Δ = (-9)² - 4(12)(4)

Δ = 81 - 192

Δ = -111

Since the discriminant Δ is negative (-111), this quadratic equation has no real solutions.

10x + y = -x² + 2

y = -x² - 10x + 2

a = -1, b = -10, c = 2

Δ = (-10)² - 4(-1)(2)

Δ = 100 + 8

Δ = 108

Since the Δ is positive and greater than zero, the equation has two real solutions.

4y - 7 = 5x² - x + 2 + 3y

4y - 3y = 5x² - x + 2 + 7

y = 5x² - x + 9

a = 5, b = -1, c = 9

Δ = (-1)² - 4(5)(9)

Δ = 1 - 20(9)

Δ = 1 - 180 = -179

No real solution.

y = (-x + 4)²

when y = 0

0 = -x + 4 or

0 = -x + 4

x = 4

The equation has one real solution.

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24 = 6kx

4 = kx

4/k = x

Let's solve for x.

3kx+24=9kx

Step 1: Add -9kx to both sides.

3kx+24+−9kx=9kx+−9kx

−6kx+24=0

Step 2: Add -24 to both sides.

−6kx+24+−24=0+−24

−6kx=−24

Step 3: Divide both sides by -6x.

[tex]\frac{-6kx}{-6x}[/tex] = [tex]\frac{-24}{-6k}[/tex]

[tex]x=\frac{4}{k}[/tex]

Answer is: 4/k

A container holds 62 cups of water how much is this in a gallon

Answer: We are given that a container contains 62 cups of water.

We are required to find how much water is contained in the container in terms of gallons.

We know that:

[tex]1[/tex] gallon [tex]=16[/tex] cups

[tex]\therefore 62[/tex] cups [tex]=\frac{62}{16}[/tex] gallons

                 [tex]=3.875[/tex] gallons

Therefore, a container contains 3.875 gallons of water.

Final answer:

To convert cups to gallons, divide the number of cups by 16 (since 1 gallon = 16 cups). For 62 cups, the conversion is 62 cups ÷ 16 cups/gallon = 3.875 gallons.

Explanation:

To convert cups to gallons, we must first know the conversion factors between these units. Using the provided reference information, we know that 1 gallon is equal to 16 cups since there are 4 quarts in a gallon and each quart is equivalent to 4 cups. Therefore, to convert from cups to gallons, we would divide the number of cups by 16.

Converting 62 cups to gallons:

So, the container holds 3.875 gallons of water.

x = 6 or x = - 1

rearrange the equation into standard form and factorise

subtract ( - 2x - 4 ) from both sides

x² - 5x - 6 = 0 ← in standard form

the factors of - 6 which sum to - 5 are - 6 and + 1

(x - 6)(x + 1) = 0

equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 1 = 0 ⇒ x = - 1

The slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (4, 9) and (6, 1).

Substitute

[tex]m=\dfrac{1-9}{6-4}=\dfrac{-8}{2}=-4[/tex]

Hey there!!

Given equation :

d(e-f) = g

Solve for d :

Dividing by ( e - f ) on both sides :

d = g / e - f which is [tex]d=\frac{g}{e-f}[/tex]

Hope my answer helps!

Answer:

Given: [tex]m\angle 1 = m\angle 3[/tex] and [tex]m\angle 2 = m\angle 3[/tex]

To prove that:

[tex]l || m[/tex]

1. [tex]m\angle 1 = m\angle 3[/tex]          [Given]

[tex]m\angle 2 = m\angle 3[/tex]

Substitution property of equality says that:

If x = y, then x can be substituted in y, or y can be substituted in x.

2 [tex]m\angle 1 = m\angle 2[/tex]          [ By Substitution Property]

Alternate interior angles states that when two lines are crossed by transversal , a pair of angles on the inner sides of each of these two lines on the opposite sides of the transversal line.

3. [tex]\angle 1[/tex] and  [tex]\angle 2[/tex] are alternate interior angles  [By definition Alternate interior angle].

Alternating interior angles theorem states that if two parallel lines are intersected by third lines, then the angles in the inner sides of the parallel lines on the opposite sides of the transversal are equal.

4. [tex]l || m[/tex] ; then the lines are parallel     [By Alternate interior angles theorem]

Correct match is as follows:

1. [tex]m\angle 1 = m\angle 3[/tex]          [Given]

 [tex]m\angle 2 = m\angle 3[/tex]

2. [tex]m\angle 1 = m\angle 2[/tex]          [Substitution]

3. [tex]\angle 1[/tex] and  [tex]\angle 2[/tex] are alternate interior angle       [By definition of alternate interior angles ]

4. [tex]l || m[/tex] the lines are parallel  [If alternate interior angles are equal]

The question involves a geometrical proof where measurements of angles are given and a conclusion regarding parallel lines need to be derived. The steps of proof are matched with relevant geometric concepts. The matching involves principles like substitution, definition of alternate interior angles, and a theorem about alternate interior angles and parallel lines.

In the context of the given problem, the matching would be as follows:

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Answer:

$96

Step-by-step explanation:

Multiply The Number Of Tickets By Amount Of People Going

16 * 6

$90/10 = 9

$160/20 = 8

$80/10 = 10

$120/20 = 6

The package that has the lowest ratio cost to number of lessons is $120 for 20 lessons.

Hope this Helps!!

The package with the lowest ratio of cost to number of lessons is the $120 for 20 lessons option, calculating to a cost of $6 per lesson, which is the most cost-effective option.

To find this, we calculate the cost per lesson for each package by dividing the total cost by the number of lessons.

Therefore, the package with the lowest ratio of cost to number of lessons is $120 for 20 lessons, with a cost of $6 per lesson.

HAVE smart phones + do NOT have smart phones = 125

Have smart phones

[tex]\frac{3}{5} *125 = \frac{3(125)}{5} = 3(25) = 75[/tex]

HAVE + NOT = 125

 75     + NOT  = 125

-75                     -75

             NOT = 50

Answer: 50 people do not have a smart phone

Answer:

It is given that Graph the image of the given triangle after the transformation that has the rule (x, y)→(−x, −y) .

From the given figure it is noticed that the vertices of the triangle are (6,7), (7,4), (-2,5).

From the given rule (x, y)→(−x, −y)  the vertices of the image are (-6,-7), (-7,-4) and (2,-5).

Plot these points on the coordinate plane.

In the below graph, the image of the given triangle is represented by green lines.

There was no change in Samuel's savings account balance. He made a deposit of $160 but after two weeks, he withdrew the same sum. He still had $20 in his account as a result.

This math query relates to fundamental financial operations. Samuel has $20 in his savings account at the start of the story. His total now stands at $180 after his subsequent $160 deposit. He withdraws $160, though, after two weeks. He now has $20 in his account after that. Finally, there was no change in Samuel's savings account balance. His account was $20 from beginning to end.

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I believe the answer is 9.8

Hope this helps :)