solve y^2+7y+12=0 by completing the square.​

Answer:

Part a) The constant of variation is [tex]r=0.0567[/tex] or [tex]r=5.67\%[/tex]

Part b) [tex]I=\$662.03[/tex]

Step-by-step explanation:

Part a) Find the constant of variation.

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

In this linear direct variation the constant r represent the constant of proportionality

where

I is the Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=5/12\ years\\ P=\$3,892\\ I=\$92\\r=?[/tex]

substitute the values and solve for r

[tex]92=3,892(r(5/12))[/tex]

[tex]r=(92*12)/(3,892*5)[/tex]

[tex]r=0.0567[/tex]

Part b) what will the interest be after 3 years

in this part we have

[tex]t=3\ years\\ P=\$3,892\\ I=?\\r=0.0567[/tex]

substitute the values

[tex]I=3,892(0.0567*3)=\$662.03[/tex]

Answer: Interquartile: 8.25

Mean: 14.5

Median: 15.5

Step-by-step explanation:

radius(r)=1cm

answer:-

diameter(d)=2r=2cm

Answer:

Step-by-step explanation:

A diameter is two times longer than a radius. Therefore, if the radius r = 1cm, then the diameter d = 2(1cm) = 2cm.

The solution to the system of equations y = x - 4 and y = 4x + 2 is found by setting the two equations equal to one another and solving for x and y. The solution is (-1.5, -5.5).

The solution to the system of equations can be found by setting the two equations equal to each other, as they are both equal to y.

Equation 1: y = x - 4

Equation 2: y = 4x + 2

To find the point of intersection, set the two equations equal to each other: x - 4 = 4x + 2. Solve this for x to get that x = -1.5. Then, substitute x = -1.5 into one of the original equations to solve for y. If we use Equation 1, we get that y = -1.5 - 4 = -5.5. Therefore, the solution to the system of equations is (-1.5, -5.5).

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The solution to the system of equations is [tex]\(x = -2, y = -6\)[/tex]. The point of intersection is [tex]\((-2, -6)\)[/tex].

The solution to a system of equations is the point where the graphs of the two equations intersect.

1. Set the Equations Equal to Each Other:

[tex]\[ x - 4 = 4x + 2 \][/tex]

2. Solve for x:

[tex]\[ -3x = 6 \][/tex]

[tex]\[ x = -2 \][/tex]

3. Substitute x back into one of the original equations to find y

[tex]\[ y = -2 - 4 = -6 \][/tex]

So, the  solution to the system of equations is [tex]\(x = -2, y = -6\)[/tex]. The point of intersection is [tex]\((-2, -6)\)[/tex].

In an isosceles triangle, the two angles at the base are the same. So, the base angles are both 54°, for a total of 108.

Since the interior angles of a triangle sum up to 180°, the remaining angle must be

[tex]180-54-54=180-108=72[/tex]

Answer:

Step-by-step explanation:

l=2w-5

2(l+w)=80

l+w=40

2w-5+w=40

3w=45

w=15 feet

l=25 feet.

the width is 15 feet and length is 25 feet.

Answer:

it is a rectangular prism

Step-by-step explanation:

it is 3D and when something has four faces that are rectangular and two that are sqaure it makes it a rectangular prism. imagine the rectangles on the sides and sqares at the end, it looks like a rectangle =).

Answer:

a) Neither arithmetic nor Geometric

Explanation:

Since 99-89.9= 9.1, and 89.9 - 78.8 = 11.1, the sequence is not arithmetic.

Like wise 89.9/99=0.908 and  78.8/89.9 = 0.876 makes it not a geomtric sequence

Step-by-step explanation:

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

99, 89.9, 78.8, 68.7, . . . . .

Here,

[tex]a_1=99\\\\a_2=89.9\\\\a_3=78.8\\\\a_4=68.7[/tex]

But we can see that there is minor difference between the consecutive terms:

So, we will go for common difference whether it is same or not.

[tex]a_2-a_1=89.9-99=-9.1\\\\a_3=a_2=78.8-89.9=-11.1\\\\a_4-a_5=68.7-78.8=-10.1[/tex]

Their difference are not common.

So, It is neither geometric nor arithmetic.

Hence, Option 'a' is correct.

Check the picture below.

notice chord QR is a diameter, thus the vertex at P has a right-angle by Thales theorem.

Answer:

0.3

Explanation:

We are given that:

Probability that a randomly chosen person lives in the East is 0.12

P(East) = 0.12 ..................> I

Probability that a randomly chosen person lives in the West is 0.18

P(West) = 0.18 ............> II

Now, we want to find the probability that the randomly chosen person lives in the East or West

To do this, we will use the following formula:

P(A or B) = P(A) + P(B)

Applying this rule to our givens:

P(East or West) = P(East) + P(West)

P(East or West) = 0.12 + 0.18

P(East or West) = 0.3

Hope this helps :)

Answer:

0.30

Step-by-step explanation:

The probability that a person chosen at random lives in the east region is 0.12

The probability that a person chosen at random lives in the west region is 0.18

The probability that a person chosen at random lives in east or west region;

[tex]P(E\:or\:W)=P(E)+P(W)[/tex]

This implies that;

[tex]P(E\:or\:W)=0.12+0.18[/tex]

[tex]P(E\:or\:W)=0.30[/tex]

Answer: d

Step-by-step explanation:

so 16+16=32

and to make things easier 32+32=64

64-8=56

The age of Julia is,

⇒ 6 years

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Dave is 8 years younger than 4 times Julia‘s age.

Let Julia age = x

Hence, Age of Dave is,

⇒ 4x - 8

Here, Age of Dave is, 16

Hence,

⇒ 4x - 8 = 16

⇒ 4x = 16 + 8

⇒ 4x = 24

⇒ x = 6

Thus, The age of Julia is,

⇒ 6 years

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B 'cause A return value equal to 0

Answer:

he did better in his History test

Step-by-step explanation:

40-28 gives you 12 marks he lost

whereas

60-39 gives you 21 makes he lost

therefore he done better in his history test the he did in his geo test because he lost more marks in his geo test then her did in his history test

Make the denominators same

take LCM of 40 and 60

120

[tex]\frac{28*3}{40*3}\\\frac{84}{120} \\\\\frac{39*2}{60*2} \\\frac{78}{120}[/tex]

Phil did better in this history test

Answer:

y = 20x

Step-by-step explanation:

We know that the car gets 20 miles per gallon and the number of miles traveled varies directly with the number of gallons of gas the tank holds.

We are to write a direct variation equation which represents this situation.

Direct variation is expressed in the form [tex]y=kx[/tex], where [tex]k[/tex] is the constant of variation.

So for this situation, the direct variation equation will be:

[tex]y=20x[/tex]

Answer: [tex]y=20x[/tex]

Step-by-step explanation:

By  definition, a direct variation equation has the form shown below:

[tex]y=kx[/tex]

Where k is a constant, y is the dependent variable and x is the independent variable.

According to the problem, you know that your car gets 20 miles per gallon. The number of miles traveled varies directly with the number of gallons of gas the tank holds.

Then, you can write the following direct variation equation that represents the situation:

y: The number of miles traveled

x:  the number of gallons of gas the tank holds.

k: 20 (Because your car gets 20 miles/gallon)

Then:

[tex]y=20x[/tex]

Answer: Last option.

Step-by-step explanation:

By definition, the square of a binomial is:

[tex](a+b)^2=a^2+2ab+b^2\\\\(a-b)^2=a^2-2ab+b^2[/tex]

Keeping the above on mind, you have the following expression given in the problem:

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

Therefore, if:

[tex]a=x\\b=5[/tex]

You obtain the following trinomial:

[tex](x+5)^2=x^2+2(x)(5)+5^2=x^2+10x+25[/tex]

Therefore, the answer is the last option.

Answer:

D. x2 + 10x + 25

Step-by-step explanation:

Answer:

The two groups collected 573.

Step-by-step explanation:

238

+345

=

573

Answer:

red is the reflection ,black is (-5,8)

Step-by-step explanation:

Answer:

the image of (-5,8) after a reflection over the y-axis is (5,8)

Step-by-step explanation:

the image of (-5,8) after a reflection over the y-axis

When a point is reflected over y axis, then the value of x changes to -x.

the value of y remains the same.

If (x,y) is reflected over y axis , then it becomes (-x,y)

The point (-5,8) after reflection over y axis it becomes (-(-5),8) that is (5,8)

the image of (-5,8) after a reflection over the y-axis is (5,8)

Answer:

the answer is 84

Step-by-step explanation:

a dozen is 12 so you take 12 times 7 and get 84

Heyaaa

The answer is 84 Candles .

There are 12 in a dozen , and there are 7 dozen.

12 x 7 = 84

Good luck :)

Answer: I can barly see that sry i cant awnser

Step-by-step explanation:

Answer:

3rd graph

Step-by-step explanation:

just that easy

Answer:

x = 7

Step-by-step explanation:

5 + 3x + 7 = 5x - 2

Solve for x and you get 7

Answer:

x = 7

Step-by-step explanation:

We are given that A, B and C are collinear points and B is in between A and C.

The length from A to B is [tex] 5[/tex], length from B to C is [tex] 3x + 7 [/tex] and AC is [tex] 5 x - 2 [/tex].

We are to find the value of x.

[tex] A B + B C = A C [/tex]

[tex] 5 + 3 x + 7 = 5 x - 2 [/tex]

[tex] 5 x - 3 x = 5 + 7 + 2 [/tex]

[tex] 2 x = 1 4  [/tex]

[tex] x = \frac { 1 4 } { 2 } [/tex]

x = 7

Answer:

JM

Step-by-step explanation:

If it is equal to each other than all you do is look at what it will be like for the other one.

A is at the beginning and D is at the end.

J is at the beginning and M is at the end.

JM is your answer.

Answer:

JM corresponds to AD.

Step-by-step explanation:

Look at their relative positions in the 2 names.

A and D are the first and last letters.

So the answer is JM because they are the first and last letters in JKLM.

Answer:

(-4,1)

Step-by-step explanation:

First, subtract 1-5. (When you move left or down you subtract. When you move right or up you add.) Left and right affect the x-axis

Second, subtract 4-3. Up and down Affect the y-axis

It would look like this:

(1,4)

=(1-5,4-3)

=(-4,1)

Answer:

here you go(image included)

Step-by-step explanation:

Answer:

1/16 of the class are left handed boys but we do not know the amount of left handed girls so we cannot be sure.

Step-by-step explanation:

1/2 * 1/8 = 1/16

there is still no way to be sure of how many girls are left handed so you should probably make a note by the problem so the mistake on the test will be realized

By multiplying the fractions, we find that 1/16 of the students in Mrs. Wallace's science class are left-handed boys.

To solve this problem, we first need to understand that it involves fraction multiplication. We know that 1/2 of the students in Mrs. Wallace's science class are boys. Out of these boys, we know that 1/8 of them are left-handed.

When you want to find out a certain amount out of a fraction, you multiply fractions. In this case, 1/2 (the number of boys in class) times 1/8 (the fraction of boys who are left-handed) gives us 1/16. Therefore, 1/16 of the students in Mrs. Wallace's science class are left-handed boys.

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Answer:

A   942

Step-by-step explanation:

3/5ths is .6

125.6 / 2 = 62.8

62.8 * 15 = 942

Answer: Its A 942 hope this helped

Answer:

3.7

Step-by-step explanation:

2.6  = 9.62/x

2.6x = 9.62     Multiplied each side by x

     x = 3.7       Divided each side by 2.6.

Answer:

[tex]\large\boxed{The\ slope=\dfrac{3}{2}}[/tex]

Step-by-step explanation:

The formula of a slope:

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

From the graph we have the points (0, 0) and (4, 6) - look at the picture.

Substitute:

[tex]m=\dfrac{6-0}{4-0}=\dfrac{6}{4}=\dfrac{6:2}{4:2}=\dfrac{3}{2}[/tex]

The slope of the line is [tex]\frac{3}{2}[/tex]

The change in y co-ordinate with respect to the change of x co-ordinate of a line is called the slope of the line.

Slope of a line is denoted by "m"

If two points on the line are [tex](x_{1},y_{1})[/tex] & [tex](x_{2} ,y_{2})[/tex], then m = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]

From the given graph, We take to points (2, 3) & (4, 6)

Now, Slope (m) = [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]

                         = [tex]\frac{6-3}{4-2}[/tex]

                         = [tex]\frac{3}{2}[/tex]

The slope =  [tex]\frac{3}{2}[/tex]

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The function which is quadratic is:

           [tex]y-3x^2=3(x^2+5)+1[/tex]

We know that the general equation of a quadratic function is given by:

[tex]y=ax^2+bx+c[/tex]

where a , b and c are real numbers.

1)

[tex]y-3x^2=3(x^2+5)+1[/tex]

On solving we get:

[tex]y-3x^2=3x^2+15+1\\\\\\y=3x^2+3x^2+1+15\\\\\\y=6x^2+16[/tex]

Hence, the function is quadratic.

2)

[tex]y^2-7x=2(x^2+6)+7[/tex]

It is not a quadratic equation since we have a term as : [tex]y^2[/tex]

and hence the equation will not match the general equation of the quadratic function.

3)

[tex]y-2x^2=6(x^3+5)-4[/tex]

as it has a term of [tex]x^3[/tex]

Hence, it is a equation of a cubic function.

4)

[tex]y-5x=4(x+5)+9[/tex]

On solving we get:

[tex]y=9x+29[/tex]

It does not has any term of [tex]x^2[/tex]

Hence, the equation is not a quadratic function it represent a linear function.

The functions that are quadratic functions are [tex]y - 3x^2 = 3(x^2+5)+1\\[/tex] and [tex]y^2-7x= 2(x^2+6) +7[/tex].

The highest power of the polynomial is called the degree of the polynomial. The polynomial of degree two is called a quadratic polynomial.

According to the question,

1)

[tex]y - 3x^2 = 3(x^2+5)+1\\ y = 3x^2+ 15 + 3x^2 +1\\ y = 6x^2 +16[/tex]

Since the polynomial is of degree 1, It is a quadratic function.

2)

[tex]y^2-7x= 2(x^2+6) +7\\y^2= 2x^2 +7x+19[/tex]

The function is a quadratic function.

3)

[tex]y - 3x^2= 6(x^3+5)-4[/tex]

The degree of x is 3, so it is a cubic function.

4)

[tex]y - 5x = 4(x+5)+9 y \\= 4x + 5x+ 29y\\ = 9x+29[/tex]

The function is a linear function.

The functions which are quadratic equations are [tex]y - 3x^2 = 3(x^2+5)+1\\[/tex]and  [tex]y^2-7x= 2(x^2+6) +7[/tex] .

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Answer:

To get the x-intercepts of the function, f(x) = 4x2 – 24x + 20

It has to be equated to zero and the values of x are the x-intercepts. So,

4x2 – 24x + 20 = 0

The resulting equation is a quadratic equation which can be solved by different methods. The solution is

x = 5, 1

The average therefore is:

(1+5/)2 = 3

The equation that represents the average of the x-intercept is 3.

Option C is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

f(x) = 4x² - 24x + 20

x-intercept is f(x) = 0.

Now,

4x² - 24x + 20 = 0

4(x² - 6x + 5) = 0

x² - 6x + 5 = 0

x² - (5 + 1)x + 5 = 0

x² - 5x - x + 5 = 0

x(x - 5) - 1(x - 5) = 0

(x - 1)(x - 5) = 0

x = 1 and x = 5

The average of x-intercept.

= (1 + 5)/2

= 6/2

= 3

Thus,

The average of the x-intercept equation is 3.

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Answer:

Five Vases

Step-by-step explanation:

In this type of questions, you can't have a reminder. You would have to round up instead.

49 flowers / 10 per case = 4 remainder 9

Because you have a remainder you need to round 4 up to 5.

You need 5 vases.