(03.01) Factor completely x2 − 12x + 35. (1 point)

Answer:

O4) x = y

Step-by-step explanation:

I took this before

Final answer:

The question pertains to writing an equation for a mathematics-related scenario, emphasizing the importance of understanding equations as expressions of concepts rather than just tools for calculation.

Explanation:

The subject of this question appears to revolve around forming an equation that could pertain to a mathematics problem. The use of mathematical equations to convey concepts is crucial; they aren't just mechanisms for inserting and churning numbers, but they are sentences that express concepts precisely and purposefully. Writing out such equations in both words and symbols ensures comprehension of the underlying reasoning.

Moreover, when teaching mathematics, it's beneficial to allow students to create their own formulas. This practice not only solidifies the understanding of concepts but also emphasizes that the symbols used in equations are arbitrary and that what matters is the concept they represent.

Remembering the correct order of operations is essential, which can be recalled with the mnemonic 'Please Excuse My Dear Aunt Sally.' Also, an iterative relation often used in advanced mathematics is not an equation per se, but rather a set of instructions for approximating a solution. This iterative process requires a different approach compared to straightforward equation solving.

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]

The equation of the function represented by the table is y = 5 x + 2

Step-by-step explanation:

The equation of the linear function in the slope-intercept form is

y = m x + b, where

The table:

→  x  :    0    :    1    :    2    :    3    :    4

→  y  :    2    :    7    :    12  :    17   :    22

Let us chose any two points from the table to calculate the slope

∵ Points (1 , 7) and (2 , 12) lie on the line

∴ [tex]x_{1}[/tex] = 1 and [tex]x_{2}[/tex] = 2

∴ [tex]y_{1}[/tex] = 7 and [tex]y_{2}[/tex] = 12

- Substitute these values in the formula of the slope

∵ [tex]m=\frac{12-7}{2-1}=\frac{5}{1}[/tex]

∴ m = 5

Substitute the value of m in the form of the equation

∵ y = m x + b

∴ y = 5 x + b

∵ The line intersects the y-axis at point (0 , b)

∵ From the table point (0 , 2) lies on the line

∴ b = 2

∴ y = 5 x + 2

The equation of the function represented by the table is y = 5 x + 2

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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:

Both monthly payment and total payment will increase.

Step-by-step explanation:

If I buy a home and make a relatively small down payment, then the due payment will be more.

If I pay for my home through a bank and I fix the number of installments to pay back the due amount after down payment (say, monthly installment for 5 years), then the amount of installment payment will definitely increase if my down payment is less.

Again, if the down payment is less, the remaining amount to pay back will rise and the bank calculates interest on the remaining amount to pay. Therefore, the amount of interest will rise in value and finally the total payment after interest for my loan will increase. (Answer)

The quadratic equation whose roots are 4 and 5, and whose leading coefficient is 4, is: [tex]\[\bo{4x^2 - 36x + 80 = 0}\][/tex]

Step 1

To write a quadratic equation with given roots and a specified leading coefficient, we can use the fact that if p and q are the roots of a quadratic equation, the equation can be written as:

[tex]\[a(x - p)(x - q) = 0\][/tex]

where a is the leading coefficient.

Given roots: [tex]\( p = 4 \)[/tex] and [tex]\( q = 5 \)[/tex]

Leading coefficient: [tex]\( a = 4 \)[/tex]

Step 2

Let's substitute these values into the equation:

[tex]\[4(x - 4)(x - 5) = 0\][/tex]

Now, we need to expand this equation. First, expand the product [tex]\((x - 4)(x - 5)\):[/tex]

[tex]\[(x - 4)(x - 5) = x^2 - 5x - 4x + 20 = x^2 - 9x + 20\][/tex]

Step 3

Next, multiply this expression by the leading coefficient [tex]\( 4 \)[/tex]:

[tex]\[4(x^2 - 9x + 20) = 4x^2 - 36x + 80\][/tex]

Thus, the quadratic equation whose roots are 4 and 5, and whose leading coefficient is 4, is:

[tex]\[\bo{4x^2 - 36x + 80 = 0}\][/tex]

Answer:

D. Both A and B are true

Step-by-step explanation:

Why would you study to decrease scores? so C. Is automatically wrong. Now A. is true and B. is true. D says both A and B are true so D is correct.

Answer:

D

Step-by-step explanation:

D. Both A and B are true.

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:

The radius of the circle is 160cm

Step-by-step explanation:

circumference of circle = 2πr

circumference = 320π cm

2πr = 320π

2r = 320

r = 160 cm

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

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Answer:

5 tablets can be bought

Step-by-step explanation:

47/8= 5

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:

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]

Answer:

No Solution.

Step-by-step explanation:

x+y=-9

x+y=5

------------

x+y=-9

-(x+y)=-5

---------------

x+y=-9

-x-y=-5

-------------

0=-14

Answer: the 2 equations are 2(pi)r and (pi)d.

Step-by-step explanation: the radius is from the center of the circle to the edge. And the diameter is double that. R is radius and d is diameter since the diameter is double the radius, you don’t need to multiply it by 2. Hope this helps!

Answer:

y = -2x - 1

Step-by-step explanation:

Formula is y = mx + b

m = slope

slope = change in y/change in x = (-1 - 3) / (0 - -2) = -4/2 = -2

So equation is now y = -2x + b

To find b, substitute any value from the table into the equation. Let's use (-2,3)

y = -2x + b

3 = -2(-2) + b

3 = 4 + b

-1 = b

So equation is y = -2x - 1

Answer:

C. This can be found by looking at when x=0. If y=-1, then that means that the y intercept is -1, so plug in 1 to either one of the middle two equations and see if it works.

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

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)

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

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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:

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.

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]

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:

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:

75%

The drawings will help

Refer to the first one to help understand the second.

Answer:

x=249

Step-by-step explanation:

1/3x-5+171=x

1/3x+166=x

166=x-1/3x

166=2/3x

x=166/(2/3)

x=(166/1)(3/2)

x=498/2

x=249

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? ;)

Answer:25,578

Step-by-step explanation:

Multiply 2,842 by 9