Principal: $750,00; annual interest rate: 5 percent. What is the interest after 6 months?

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

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

This is how you would graph your function.

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.

Learn more about solutions of quadratic equations here: https://brainly.com/question/1214333

#SPJ4

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.

https://brainly.com/question/29482749

#SPJ2

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:

729 = s^3

9^3 = s^3

s = 9 in.

Answer:

$96

Step-by-step explanation:

Multiply The Number Of Tickets By Amount Of People Going

16 * 6

Hello,

Please, see the attached files.

Thanks.

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

$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:

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:

https://brainly.com/question/31408211

#SPJ2

I believe the answer is 9.8

Hope this helps :)

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

[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]

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.

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.

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]

(c) multiply by 0.4

given [tex]\frac{x}{0.4}[/tex] = 10

multiply both sides by 0.4 to eliminate the fraction

x = 0.4 × 10 = 4

and [tex]\frac{4}{0.4}[/tex] = 10

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.

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.

Yuri will have 1/7 of a bag of carrots left. This is because half of 2 is 1.

The pen should be built with dimensions of 9 meters by 6 meters, with the wall forming one of the 9-meter sides.

To find the dimensions of the pen that will give the maximum area, we can use the fact that for a given perimeter, a square has the maximum area. Since one side of the pen is formed by a wall, we have 36 meters of fencing for the other three sides. Let's denote the length of the pen as [tex]\( l \)[/tex] and the width. The perimeter  of the three sides that need fencing is given by:

[tex]\[ P = l + 2w \][/tex]

 We know that the total length of the fencing available for these three sides is 36 meters, so:

 [tex]\[ l + 2w = 36 \][/tex]

To maximize the area, we want [tex]\( l \)[/tex] to be as close to [tex]\( w \)[/tex] as possible, which means we want to divide the 36 meters of fencing equally among the three sides. If we let \( w = w \), then the equation becomes:

[tex]\[ l + 2l = 36 \][/tex]

[tex]\[ 3l = 36 \][/tex]

[tex]\[ l = \frac{36}{3} \][/tex]

[tex]\[ l = 12 \][/tex]

However, this would mean that there is no fencing left for the width, as all 36 meters would be used for the length. To avoid this, we need to distribute the fencing so that two of the sides (the widths) are equal and the remaining side (the length) is the third side. To find the maximum area, we set [tex]\( l = 2w \)[/tex], which gives us:

[tex]\[ 2w + 2w = 36 \][/tex]

[tex]\[ 4w = 36 \][/tex]

[tex]\[ w = \frac{36}{4} \][/tex]

[tex]\[ w = 9 \][/tex]

 Now, we can find the length [tex]\( l \):[/tex]

[tex]\[ l = 2w \][/tex]

[tex]\[ l = 2 \times 9 \][/tex]

[tex]\[ l = 18 \][/tex]

However, since we initially assumed[tex]\( l = 2w \)[/tex] to find the width, we need to adjust the length to account for the actual fencing used. We have two widths and one length, so the correct equation is:

[tex]\[ l + 2w = 36 \][/tex]

[tex]\[ 18 + 2 \times 9 = 36 \][/tex]

[tex]\[ 18 + 18 = 36 \][/tex]

[tex]\[ 36 = 36 \][/tex]

Therefore, the dimensions of the pen are 9 meters by 6 meters, with the wall forming the side of 18 meters.

 The final answer is that the pen should be built with dimensions of 9 meters by 6 meters, with the wall forming one of the 9-meter sides.

$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.

I would travel 40hours.  16 times two is 32 plus 8 is 40.

Your answer is 5/2.

Steps:

Convert element to fraction

Multiply fractions

Cancel the common factor (1)

--

Hope this helped!