Factor −1/2 out of −1/2x+6.
The factored expression is

Answer:

The required rate of interest   =   14.285%

Step-by-step explanation:

Here, The principal amount = 7,000

The final paid amount = 9,000

Time = 2 years

Let us assume the rate of interest = R

Now, Simple Interest  =  Amount - Principal

                                      =  9,000 - 7,000  = 2,000

So, the SI on the given principal for 2 years  = 2,000

[tex]\textrm{SIMPLE INTEREST } = \frac{P \times  R \times T}{100}\\\implies 2000 = \frac{7,000 \times  R \times 2}{100}\\\implies R = \frac{2,000 \times 100}{7,000 \times 2}  = 14.285[/tex]

or, R =  14.285%

Hence, the required rate of interest   =   14.285%

Answer:

slope = - 7

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 4 = - 7(x - 6) ← is in point- slope form

with slope m = - 7

Answer:

x < 3

Step-by-step explanation:

We are given an equation of inequality of single variable x.

So, we have to solve the inequality and get the solution in terms of another inequality.

The given equation is 9 + 2x > 5x

⇒ 9 > 5x - 2x

⇒ 9 > 3x

⇒ 3x < 9 {Since if a > b then we can write b < a as they means the same.}

⇒ x < 3 (Answer)

{Dividing both sides of an inequality with a positive number need no change in inequality sign}

Answer:

Small list number of buses [tex]=3[/tex],the orchestra can rent.

Step-by-step explanation:

Form an equation representing the number of vehicles needed.

Let the number of buses be [tex]x[/tex] and the number of vans be [tex]y[/tex]

We have six drivers so,

[tex]x + y\leq 6[/tex] for both vehicles.

And it's an inequality,where we can equate with by removing the inequality to close in our answer.

[tex]x + y = 6[/tex]

Then form an equation representing the total number of seats [tex]K[/tex] in vehicles for the orchestra members.

[tex]25[/tex] people for bus and [tex]12[/tex] people for vans can be written in terms of seats.

So,[tex]K = 25x + 12y[/tex]

In terms of an inequality it can be written as,

[tex]25x + 12y\geq111[/tex],[tex]111[/tex] is the maximum numbers of the orchestra.

Solving the system of inequality.

We have

[tex]x + y = 6[/tex]

Re-arranging y.

[tex]y = 6 - x[/tex]

Plugging the values in [tex]25x + 12y\geq111[/tex] by removing the inequality and considering it as an equation.

[tex]111 = 25x + 12y = 25x + 12(6-x)[/tex]

[tex]111 = 25x + 72 - 12x[/tex]

[tex]111 - 72 = 13 x[/tex]

[tex]39 = 13 x[/tex]

[tex]x = 3[/tex]

So small list number of buses are [tex]3[/tex] there orchestra can rent.

Use [tex]\frac{a^n}{a^m}=a^{n-m}[/tex].

[tex]

\dfrac{2m^2t^6}{m^4t^2}=2m^{2-4}t^{6-2}=\boxed{2m^{-2}t^4}

[/tex]

Hope this helps.

Answer:

2m⁻²t⁴

Step-by-step explanation:

Rule:

If aᵇ / aˣ, then aᵇ ⁻ ˣ

[tex]\frac{2m^2t^6}{m^4t^2} = 2 m^{2-4} t^{6-2} = 2m^{-2} t^{4}[/tex]

Answer:

The actual length of 60 cm is modeled as 1 cm length.

Step-by-step explanation:

The diameter of the sweep of the main rotor of the helicopter is 18.6 meters i.e. 1860 cm.

Now, the toy model of the helicopter has a sweep of 31 cm.

Therefore, the scale in which the model is made is 1860 : 31 i.e. 60 : 1 ratio.

So, the actual length of 60 cm is modeled as 1 cm length. (Answer)

Answer:

The scale of the model to the actual is 1:60

Step-by-step explanation:

The scale of the model may be computes as the ratio of the diameter of the original sweep to the diameter of the model. Given that the diameter of the sweep of the main rotor of the eh101 helicopter is 18.6 meters and that of the model is 31 cm, the scale of the model

= 31cm to 18.6m

since 100cm = 1m,

18.6m = 18.6 * 100cm

= 1860 m

31cm to 18.6m = 31cm to 1860cm

= 1 to 60

Answer:

Step-by-step explanation:

Following are the response to the given table:

Therefore, the final answer is "[tex]\bold{y=x+2 \ and \ 22}[/tex]".

Learn more:

brainly.com/question/11947204

Option A: 21 pairs is the right answer

Step-by-step explanation:

Given

total strength of cycling team = 7

Captains to be selected = 2

As the order of selection doesn't matter, the combinations will be used to get the number of ways the pair can be chosen

Combination is solved as:

[tex]C(n,r) = \frac{n!}{r!(n-r)!}[/tex]

Here

n=7

r = 2

[tex]C(7,2) = \frac{7!}{2!(7-2)!}\\C(7,2) = \frac{7!}{2!*5!}\\=21\ pairs[/tex]

Hence,

Option A: 21 pairs is the right answer

Keywords: Combination

Learn more about selection at:

#LearnwithBrainly

Answer:

19 blocks

Step-by-step explanation:

To amanda's house, it is 5 blocks (we count 1 to 6 = 5 units)

From amanda's to Karen's, is 6 units (we count from -1 to 5 = 6 units)

Now, to find Karen to own place, we have to use the Pythaogrean Theorem. It is applicable for right triangle (which is shown, Amanda's place is the right angle).

The two distance we found are the two legs of the triangle and the other side (what we need to find) is the hypotenuse (which is the side opposite of right angle). The theorem says:

Leg^2 + Another Leg^2 = Hypotenuse^2

We know the 2 legs' length, so we can solve for hypotenuse (Karen to Own place Distance). Shown below:

[tex]5^2 + 6 ^ 2 \\=25+36\\=61[/tex]

So, we have:

Hypotenuse^2 = 61

Hypotenuse = Sqrt(61) = 7.81

Rounded to nearest block, that is 8 blocks

So, total distance traveled is:

5 + 6 + 8 = 19 blocks

Answer:

Length of the rectangle is [tex]18.85\ inches[/tex],and the width of the rectangle is [tex]16.35\ inches[/tex]

Step-by-step explanation:

Let the width of the rectangle be [tex]x[/tex] inches

Then

The length of the rectangle will be [tex]x+2.5[/tex] inches

So perimeter [tex]=2(length + width)[/tex]

Plugging the values:

⇒ [tex]2(x+x+2.5)=75.4[/tex]

⇒ [tex]2(2x+2.5)=75.4[/tex]

⇒ [tex]4x+10=75.4[/tex]

  Subtracting [tex]10[/tex] from both sides.

⇒ [tex]4x=65.4[/tex]

⇒ [tex]x=\frac{65.4}{4}=16.35\ inches[/tex]

  So the width of the rectangle is [tex]16.35\ inches[/tex]

   And the length of the rectangle is [tex]18.85\ inches[/tex]

If Jeffrey takes 50 classes in his first month as an instructor, he will earn back the amount he spent on certification.

Step-by-step explanation:

Amount spent on certification = $200

Base salary = $50

Payment per class = $3

Let, x be the number of classes.

J(x) = 50+3x  

He needs to earn $200 dollars in first month, therefore,

50+3x=200

[tex]3x=200-50\\3x=150[/tex]

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{150}{3}\\x=50[/tex]

If Jeffrey takes 50 classes in his first month as an instructor, he will earn back the amount he spent on certification.

Keywords: function, linear equation

Learn more about functions at:

#LearnwithBrainly

Answer:

399.409

Step-by-step explanation:

Add both numbers to get your answer.

Answer:

The answer is

399. 409

Answer:

600 students

Step-by-step explanation:

100% - 24% = 76%

76% = 456

100%= x

76x = 456x100

x = 45600÷76

x= 600 students (total)

Answer: 600

Step-by-step explanation:

Since there are 24% of boys in a school , this means that the number of girls will be :

100% - 24 %

= 76%

That means there are 76% of girls in the school.

Let the total number of students in the school be x, this means that

24% of x = number of boys

76% of x = number of girls

Since the total number of girls is given to be 456 , then

76% of x = 456

0.76x = 456

x = 456/0.76

x = 600

That means there are 600 students all together in the school

Answer:

(x-2)(x+2)(x^2 + 4)

Step-by-step explanation:

This can be done by difference of squares:

(x^2 - 4) (x^2 + 4)

And now (x^2 - 4) can be further factored:

(x-2)(x+2)(x^2 + 4) is your answer

Clearly, There are only 2 zeroes that we can get from this, 2 and -2

Hope this helps!

If you think I helped please mark brainliest! Would really appreciate!

Answer:

[tex]\large\boxed{x^4-16=(x^2+4)(x+2)(x-2)}[/tex]

[tex]\large\boxed{g(x)=x^4-16\ \text{has two real zeros}\ x=-2\ \text{and}\ x=2}[/tex]

Step-by-step explanation:

[tex]x^4-16=x^4-2^4=x^{(2)(2)}-2^{(2)(2)}\\\\\text{use}\ (a^n)^m=a^{(n)(m)}\\\\=(x^2)^2-(2^2)^2\\\\\text{use}\ a^2-b^2=(a+b)(a-b)\\\\=(x^2+2^2)(x^2-2^2)=(x^2+4)(x+2)(x-2)[/tex]

The zeros of g(x):

[tex]g(x)=x^2-16=(x^2+4)(x+2)(x-2)\\\\g(x)=0\iff(x^2+4)(x+2)(x-2)=0\iff x^2+4=0\ \vee\ x+2=0\ \vee\ x-2=0\\\\x^2+4=0\qquad\text{subtract 4 from both sides}\\x^2=-4\qquad\bold{FALSE}\\\\x+2=0\qquad\text{subtract 2 from both sides}\\\boxed{x=-2}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}[/tex]

Answer:

I'm pretty sure this is undefined. It's either it does or does not equal to 200..

Step-by-step explanation:

n/a

Answer:

(a) 3, (b) 3

Step-by-step explanation:

HCF is highest common factor. Each number is split into multiples while the common factors are then multiplied together.

(a) HCF of 15, 63, 99

15 = 3 X 5     ----------------------------- (i)

63 = 3 X 3 X 7 ---------------------------(ii)

99 = 3 X 3 X 11 ---------------------------(iii)

From the three equations, 3 is the only common factor; 3 appears in equations (i), (ii) and (iii)

hence the HCF of 15, 63 and 99 is 3

(b) HCF of 66, 33, 78

66 = 2 X 3 X 11     ----------------------------- (iv)

33 =        3 X 11 ---------------------------(v)

78 = 2 X 3 X 13 ---------------------------(vi)

From the three equations, 3 is still the only common factor; 3 appears in equations (iv), (v) and (vi)

hence the HCF of 166, 33, 78 is 3

Answer:

Center (2,4) , radius=3, h=2 v=4 & r=3

Step-by-step explanation:

Ok so in order to find the center of the circle, use the graph (like you can see that the x is 2,if you count down from 5 to the left. the y is 4,because it's below 5 in the y pole).So the center is (2,4)

Now, in order to find the length of the radius, you need to do the following:

Take the center point (2,4) and the point where the circle ends (2,1) . Because radius is a straight, you can substract the y values of the two points : 4-1=3

As you can see in the equation, the h symbolizes the x of the center point and the v symbolizes the y.The r is the radius that we already found(3)

So it's shouldn't be a problem now to find the equation of the circle,simply replace the values with their numbers:

(x-2)^2 + (y-4)^2 = 9

The center is at (2, 4). The radius is 3 units. The value of h, v, and r are 2, 4, and 3 respectively. The standard equation of the circle is (x - 2)² + (y - 4)² = 9.

The required value can be found by counting the coordinates from the given graph.

A diagram is provided. We should observe the diagram, we can see that the center of the circle is at (2,4) on the graph.

We can also find that the radius of the circle is 3 units by counting the lines.

The center of the circle is denoted by (h, v) = (2, 4). The radius r is 3 units.

We have found the center and the radius. We can use this to make the standard equation of the circle.

The standard equation of a circle is given by:

(x - h)2 + (y - v)2 = r2

Now substitute the values h, v and, r:

(x - 2)² + (y - 4)² = 9

Therefore, we have found that the center is at (2, 4)and the radius is 3 units. The value of h, v, and r are 2, 4, and 3 respectively. The standard equation of the circle is (x - 2)² + (y - 4)² = 9.

Learn more about the standard equation of the circle here: https://brainly.com/question/1506955

#SPJ2

Answer:

The land which are used for exhibits are 89 acres (approximately).

Step-by-step explanation:

Given:

Village is spread across 240 acres of land. 37%  of land is used for the exhibits.

Now, we have to find acres of land which are used for exhibits.

So, here it is given that land used for exhibits is 37%, and we have to calculate the quantity from the percentage given:

According to question:

37% of 240 acres of land.

[tex]\frac{37}{100}\times 240[/tex]

[tex]0.37\times 240[/tex]

[tex]88.80[/tex]

So, the land used for exhibits are 88.80 acres.

Therefore, the land which are used for exhibits are 89 acres (approximately).

Answer:

x = 4

Step-by-step explanation:

It is given that [tex]\sqrt{(x - 3)} = \sqrt{x} + 3[/tex], and we have to solve the given equation for x.

Now, we have [tex]\sqrt{(x - 3)} = \sqrt{x} + 3[/tex]

Squaring both sides we get  

[tex][\sqrt{(x - 3)}] ^{2} = [\sqrt{x} + 3]^{2}[/tex]

⇒ x - 3 = x + 6√x + 9 {Since we know the formula of (a + b)² = a² + 2ab + b²}

⇒ 6√x = - 12

⇒ √x = -2

Again squaring both sides we get  

⇒x = 4 (Answer)

Answer:

3.1622776 OR √ 10

Step-by-step explanation:

The result can be shown in multiple forms.

Exact Form:

√ 10

Decimal Form:

3.16227766

3.1622776

Step-by-step explanation:

[tex]\sqrt{10}-\text{it's an irrational number}\\\\\text{You can only have an approximation}\ \sqrt{10}\approx3.1623[/tex]

Answer:

The transformation used here is,

(x, y) → (-x , -y)

Step-by-step explanation:

Triangle ABC is rotated to create the image of triangle A'B'C'

Co-ordinates of A, B, C are,

A = (-1 , -1) ; B = (1 , -1) ; C = (0, -4)

Co-ordinates of A' ,B' , C' are,

A'= (1 , 1) ; B' = (-1 , 1) ; C' = (0, 4)

Hence, the transformation used here is,

(x, y) → (-x , -y)

Answer:

(x, y) → (–x, –y)

Step-by-step explanation:

Coordinates of triangle ABC:

A (-1, -1)

B (1, -1)

C (0, -4)

If we apply the transformation (x, y) → (–x, –y) we will get:

A (-1, -1) → (1, 1)   which correspond to point A'

B (1, -1) → (-1, 1)   which correspond to point B'

C (0, -4) → (0, 4)   which correspond to point C'

The vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x. If the vertical line you drew intersects the graph more than once for any value of x then the graph is not the graph of a function.

Answer:

75%

The drawings will help

Refer to the first one to help understand the second.

Answer:

the value of x is (-2) and y is (-5)

An equation that represents the relationship between the x and y-values is y = 75x.

Erin can pick 75 apples per hour.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 75/1 = 150/2

Constant of proportionality, k = 75.

Therefore, the required linear equation that models the graph can be written as follows;

y = kx

y = 75x

Read more on proportional relationship here: brainly.com/question/28350476

#SPJ3

Answer:

5 tablets can be bought

Step-by-step explanation:

47/8= 5

The simplification of the equation when  x = -94 and y = 24 will be B: -70

Usually, simplification involves proceeding with the pending operations in the expression. Simplification usually involves making the expression simple and easy to use later.

We have been given an equation as x + y

We have to find the solution when  x = -94 and y = 24

Therefore, substitute the values;

x + y = (-94  +24)

Now Evaluate;

(-94  +24) = -70

Hence, the correct answer is B.

Therefore, The simplification of the equation when  x = -94 and y = 24 will be B: -70

Learn more about simplification;

https://brainly.com/question/17579585

#SPJ2

Answer:

a= 15

b=1/3

Step-by-step explanation:

15=a*(b)^0

15=a    

5=a*b

5=15*b       (  since, we have found that a=15 from the before steps)

5/15=b=1/3

a= 15

b=1/3.

Answer:

p = (200 -5s)/11

Step-by-step explanation:

I think you meant p is the price of piranhas, and a is the price of one shark.

You have:

11p + 5s = 200

11p = 200 - 5s

p = (200-5s)/11

Does that help? ;)