Please help with this

Answer:

(y + 6)(y + 13) = y² + 19y + 78

Step-by-step explanation:

[tex] \rm \implies (y + 6)(y + 13) \\ \\ \rm \implies y(y + 13) + 6(y + 13) \\ \\ \rm \implies {y}^{2} + 13y + 6y + 78 \\ \\ \rm \implies {y}^{2} + 19y + 78[/tex]

If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Hannah contributes £750 and following 4 years has £844.13. Then the compound interest rate is given as,

844.13 = 750 (1 + r)⁴

(1 + r)⁴ = 1.1255

1 + r = 1.02999

r = 0.0299

r = 2.99%

r ≈ 3%

If the amount after 4 years is 844.13. Then the rate of the compound interest will be 3%.

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The function f(x) = 2x + 1 has its value of x to be 3 when f(x) = 7

From the possible question, the definition of the function is given as

f(x) = 2x + 1

Also, from the question, we have:

f(x) = 7

Substitute 7 for x in the equation f(x) = 2x + 1

So, we have the following representation

2x + 1 = 7

Subtract 1 from both sides of the equation

This gives

2x = 6

Divide both sides by 2

x = 3

So, we can conclude that the value of x is 3

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Possible question

Given the function below, find the value of x if f(x)=7

f(x) = 2x + 1

Answer: 16

Step-by-step explanation:

Answer:

Step-by-step explanation:

Peter=x

Phillippa= 3x then x

Palvin= 10 then Phillippa

Step 2: Answer: Phillipa 3x+x+10

By graphing, the solution of the system of equations is: (6, -2).

To solve the system of equations by graphing, plot each of the line of the equations, then find the coordinates of the point where both lines intersect. Where they intersect is the solution to the systems of equations.

Given the following equations:

x + 2y = 2

y = -x + 4

x + 2y = 2 can be rewritten as y = -1/2x + 1. The graph for x + 2y = 2 will intercept the y-axis at 1 and also has a slope of -1/2. (It is the red line in the image below).

The graph of y = -x + 4 will also have a slope of -1 and intercept the y-axis at 4. (It is the blue line in the image below).

The graph of the equations are shown below, and they intersect at (6, -2), which is the solution to the system of equations.

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Answer:

1 piece = 1 slice then the answer is 4/3 = $1.33 (still … 3 slices will be $3.99 rounded to 4). A pizza costs £5.50 and fries cost £1.00, John orders 3 pizzas and 5 fries but the …

Answer:

$1925

Step-by-step explanation:

So your problem is $55,000 x 3.5%

You can rewrite this as:

55,000 x 3.5/100 or 55,000 x 35/1000

Now multiply. I will remove the /1000 for now.

55,000x35=1925000

Now, divide 1925000 by 1000.

1925/1000=$1,925

Answer:

y=100t+1200, where t is years since 2013 and

Step-by-step explanation:

We only have two points from which to form an equation.  Since we are told that it is a linear equation, two points is all we need to find an equation in the form of y=mx+b, where m is the slope (the rate of change) and b is the y-intercept (the value of y when x=0).  Let's make the x axis the year and y the student population.

Let's put the data into an x,y format, but before we do, lets be sure to adopt the problem's fervent wish that we treat the x variable, t, as the years since 2013.  "t is the number of years after 2013."  (0,1200) becomes is the data point for 2013.  The school's population will be the y-axis.

(0,1200)   [primary school had 1200 students enrolled in 2013], and

(3,1500)   [1500 students in 2016]

---

First calculate m, the slope.  Slope is the Rise/Run between the two points (the change in y over the change in x)

Going from (2013,1200) to (2016,1500) we find that:

  Rise  (in y) = (1500 - 1200) = 300 students

  Run  (on x) = (2016 - 2013) =     3 years

The Rise/Run, or slope, m, is 300/3 or 100:  m = 100

Lets put that into our equation format:

y = 100x + b

X will be the time, in years.  The problem asks that we define x in terms of years after 2013, and that this be assigned the variable, t:

y = 100t +b, where t is years after 2013.

(The 100 tells us that the student population increases by 100 per year)

We now need b, the y-intercept.  One can either graph this and look for the value of y when x=0, of simply input either of the data points.  This looks easy enough to input a point and solve for b:

Remember that t is the (year - 2013)

y = 100t +b   Solve for (2013,1200)

 t = 2013 - 2013 = 0

1200 = 100*(0) + b

b = 1200

Actually, b was easy enough to find without either calculating or graphing, since one of our two points tells us the y-intercept (0,1200).

The equation becomes y = 100t + 1200

See the attached graph.

It is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.

Given, a large number of MBA applicants are given an aptitude test. scores are normally distributed with a mean of 460 and standard deviation of 80.

We are asked the probability that an applicant scores below 552.

Now, using the formula of probability, we get

P(X < 552) = 0.8329

when the mean is given i.e. 460 and standard deviation is given i.e. 80.

Hence, it is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.

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There are 18 students who like snickers but not twix or reese's peanut butter cups.

Given, that 500 high school students was taken to determine their favorite chocolate candy.

118 like snickers, 185 like twix, 179 like reese's peanut butter cups,

60 like snickers and twix, 87 like twix and reese's peanut butter cups, 57 like snickers and reese's peanut butter cups,

and 17 like all three kinds of chocolate candy.

Let A = Set of students like snickers

B = Set of students like twix

C = Set of students like reese's peanut butter cups

Now, we have to find the number of students like snickers but not twix or reese's peanut butter cups i.e. A - A∩B - A∩C + A∩B∩C

A - A∩B - A∩C + A∩B∩C = 118 - 60 - 57 + 17

A - A∩B - A∩C + A∩B∩C = 135 - 117

A - A∩B - A∩C + A∩B∩C = 18

Hence, there are 18 students who like snickers but not twix or reese's peanut butter cups.

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The amount you pay for the items is C. $41.42.

The amount that the customer pays for the two items is determined by first discounting the second item by 60%.

The result after the discount is added to the cost of the first item before the sales tax is added to get the final cost of the items.

Discount on second item = 60%

The price of the first item purchased = $30

The price of the second item purchased = $20

Discounted price on the second = $8 ($30 x (1 - 60%)

Total cost before sales tax = $38 ($30 + $8)

Sales tax = 9%

Total cost after sales tax = $41.42 ($38 x 1.09)

Thus, after discounting the second item by 60% and adding the sales tax of 9%, the customer will pay $41.42 for the items.

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Answer:

c. 41.42 my teacher told me the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

We know that perpendicular lines have opposite-reciprocal slopes.

Given line:

Its slope is 2 and the perpendicular line has a slope of - 1/2.

Let's find the line with the slope of - 1/2:

Answer:

c

Step-by-step explanation:

For some n or x value, neither equation can equal 107. f(x) = 2x + 7 or

t(n) = 2n + 7.

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The value of x for the given parallelogram is 4.8 cm.

According to the question,

We have the following information:

We have a parallelogram with base x cm, height 2.5 cm and area 12 square centimeters.

(More to know: in a parallelogram, the opposite sides are equal and parallel to each other. Opposite angles of parallelogram are equal and the sum of consecutive angles is 180°.)

We know that the following formula is used to find the area of the parallelogram:

Area of parallelogram = Base*height

x*2.5 = 12

x = 12/2.5

x = 4.8 cm

Hence, the value of x is 4.8 cm.

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Answer:

The answer is w= -1

Step-by-step explanation:

4w + 2 + 0.6w = -3.4w - 6

4.6w + 2 = -3.4w - 6

8w + 2 = -6

8w = -8

w = -1

Answer:

5.68 ft

Step-by-step explanation:

12 inches = 1 feet

[tex]68 \: inches \: *\: \frac{1 feet}{12 \: inches} =\frac{68}{12} \: feet= 5.6777...\\\\68 \: inches \approx 5.68 \: feet[/tex]

It takes 35 years for the population of West Fremont to double. We have the following condition;

West Fremont is a tiny town with 50,000 residents. If West Fremont experiences 2% growth. To solve the given case to get how long it takes for the population of West Fremont to double.

Here, we use the rule of 70 case. The rule of 70: By dividing the number 70 by the growth rate of the variable, the rule of 70 may be used to calculate how many years it will take for a variable to double.

According to the yearly rate of return, the rule of 70 is typically used to calculate how long it would take for an investment to double.

Doubling time = 70 / Growth rate                

= 70 / 2                        

= 35 years

So, it takes 35 years for the population of West Fremont to double.

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The equation which can be used to find how much fabric is used in each bandana is [1/2 ÷ 6 = x].

So, the equation to get fabric used in each bandana:

Then, the fabric in each bandana will be:

Solve as follows:

So, 1/12 yards of fabric is used in each bandana.

Therefore, the equation which can be used to find how much fabric is used in each bandana is [1/2 ÷ 6 = x].

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Complete question:

The drama teacher is making bandanas for costumes. She is cutting 1/2 yard of fabric into 6 bandanas of the same size. Write and solve an equation to find how much fabric there will be for each bandana.

The correct inequality symbol that makes the statement true is:

1000 < (6²)³.

The inequality symbols, and their meaning, are presented as follows:

In the context of this problem, the numbers being compared are presented as follows:

1000 and (6²)³.

The power of power property of a number with multiple exponents means that the base is kept while the exponents are multiplied.

The number in which this property is applied in this problem is (6²)³, in which:

Hence the equivalent number is given as follows:

(6²)³ = 6^6 = 6 x 6 x 6 x 6 x 6 x 6 = 46,656

Which is a greater number than 1,000, meaning that 1,000 is less than the number, and the inequality is:

1000 < (6²)³.

The problem is given by the image at the end of the answer.

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From the coefficients of the quadratic equation and the vertex of the parabola, it was found that the graph again crosses the x-axis  in x=7.

The standard form for a quadratic equation is ax²+ bx + c=0, where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving the quadratic function, you should find the discriminant: Δ=b²-4ac and then use this variable in the formula: [tex]\frac{-b \pm \sqrt{\Delta} }{2a}[/tex] .

The given equation is a quadratic function because have a degree equal to 2. Therefore, the graph is represented by a parabola. The vertex of the parabola is given by the coordinates(xv= -b/2a, yv= -Δ/4a).

From the given figure, it is possible to see that:

For x= -1, you have y=0, then:

ax²+bx+c=0 -> x=-1

a (-1)²-b+c=0

a*1-b+c=0

a-b+c=0 (1)

For y= 2, you have x=0, then:

ax²+bx+c=0

a*0²+b*0+c=2

0+0+c=2

c=2 (2)

As, a-b+c=0 (1) and c=2 (2), you have:

a-b+c=0

a-b+2=0

a-b=-2 (3)

Now, you should use the information about the xv.

[tex]x_v=\frac{-b}{2a} =3[/tex]

-b=6a

b=-6a

From equation 3, you will find the coefficient a .

a-b=-2 (3)

a-(-6a)= -2

a +6a =-2

7a= -2

a=-2/7

If a= -2/7, from equation 3 you can find the coefficient b.

b=-6a = -6* (-2/7)=12/7

Thus, the quadratic equation of the plot is: ax²+bx+c

[tex]f(x)=-\frac{2}{7}\cdot \:x^2+\frac{12}{7}\cdot \:x+2[/tex]

Now, you should find the roots for the found equation :[tex]f(x)=-\frac{2}{7}\cdot \:x^2+\frac{12}{7}\cdot \:x+2[/tex].

[tex]x_{1,\:2}=\frac{-12\pm \sqrt{12^2-4\left(-2\right)\cdot \:14}}{2\left(-2\right)}[/tex]

[tex]x_1=\frac{-12+16}{2\left(-2\right)}=-1,\:x_2=\frac{-12-16}{2\left(-2\right)}=7[/tex]

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The following are features of the parabola shown in the diagram:

Vertex:  (2, -1)

Axis of symmetry: x = 2

The parabola opens downward.

The vertex of a graph is the coordinates of the point where the tip of the parabola lies at.

What is the Axis of Symmetry of a Parabola?

The axis of symmetry of a parabola passes through the vertex and is it expressed as the x-coordinate of the vertex of the parabola.

The tip of the parabola shown in the image above is at (2, -1), and the parabola as can be seen opens downward.

Therefore:

The vertex of the parabola is (2, -1)

The axis of symmetry would be expressed as x = 2. The parabola opens downward as well.

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The probability that he is a male civilian employee is 0.13362.

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. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given that 66% of full-time law enforcement employees are sworn officers, 34% of them are civilian employees (100 - 66).

Given that 60.7% of civilian employees are women. Therefore, the percentage of men is (100 - 60.7)% or 39.3%.

Therefore, the likelihood that he works as a male civilian is 39.3% of 34%, which equals 0.393 * 0.34, = 0.13362.

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Exactly one type of meat required = 5 choices

acc  to our question-

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The number of cells cut into two by the diagonal of the rectangle, found by using Pythagorean theorem, are approximately 51 cells

Pythagorean theorem can be expressed as the square of the hypotenuse side of a right triangle is equal to the sum of the square of the legs of the triangle.

The dimensions of the rectangle = 60 units by 40 units

The dimensions of each grid = 1 unit by 1 unit

The vertices of the rectangle are (0, 0), (60, 0), (60, 40), (0, 40)

The slope of the diagonal is therefore;

m = 40/(60) = 2/3

The equation of the line is; y - 0 = 2/3·(x - 0) = 2/3·x

y = 2/3·x
The number of cells in the diagonal is found using Pythagorean theorem as follows as follows;

Length the diagonal, l = √(60² + 40²) ≈ 72.1

Length of the diagonal of a unit = √(1 + 1) =√2

Number of units in the diagonal, n = 72.1/√(2) ≈ 51 units

The number of cells  cut into two ≈ 51 cells

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An area 825 by 550 ft gives max area for $6600.

acc to our question-

hence, 3300 + 3300 = $6600

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The equation 22+(d-1)0.5 = 30 may be used to determine how many days it will take the plant to reach a height of 30 cm. The value of d is 17, and it stands for the number of days.

There are two definitions for an arithmetic sequence. It is a series where the differences between every two succeeding terms are identical or each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term.

The following details are available to us:

A 22 cm tall basil plant that is gaining half a centimeter daily was purchased by Matteo.

We now have the arithmetic progression shown below with the common difference, indicated by the letter d:

22, 22.5, 23, 23.5, ...

The formula for calculating the nth term:

When an is the first term, a(n) = a+(n-1)d.

A) 22+(d-1)0.5 = 30

B) The plant still needs to develop 8 cm, as there is a difference of 8 cm between 30 and 22.

C) D's value:

22+(d-1)0.5 = 30

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Answer:

Yes it is

Step-by-step explanation:

Every new number is 3 less than the last number

n-3

Answer:

Yes, -3

Step-by-step explanation:

An arithmetic sequence is when the numbers in the sequence are subtracted or added by the same value everytime to get the next number. (NOT multiplied or divided, if it's that then it's a geometric sequence)

from 36 to 33, we can see the change is -3
from 33 to 30, it's also -3
from 30 to 37, it's also -3

The common difference is the difference between the two consecutive terms in the sequence, which is -3

Since it's subtracting or adding by the same value everytime to obtain the next value, this sequence is an arithmetic sequence, and the common difference is -3

Answer:

3 feet

1ft:2ft

Step-by-step explanation:

3ft/12 inches

12 inches= 1 foot

We can simplify the denominator by turning 12 inches into 1 foot

3/1

And then we divide to make 3 feet

The width of the rectangle is 12 inches and the length is 2 feet so the ratio is

12 in.:2 ft

12 inches can be simplified to 1 foot

1 ft: 2 ft

And it is simplified as much as possible

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