Find x
35°
100°
X
algebra 1

The algebraic proof that 10+n²-(n - 2)² is always an even number is 2(5+(2n-2))

To show that this will always give an even number, we need to express in a form that it is 2 multiplied by some positive integer

Given: n is an integer greater than 1, prove 10+ n² - (n - 2)² algebraically

10+ n² - (n - 2)² = 10+ ( n² - (n - 2)² )      (factorize difference of two squares)

                     = 10+(n-(n-2))(n+(n-2))      

                     = 10+(n-n+2)(n+n-2)         (simplify)

                     = 10+(2)(2n-2)                  (factorize)

                     =  2(5+(2n-2))

Therefore, due to the factor of 2, the given expression is always even for integer n

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The function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

The quadratic function is

f(x) = [tex]-3x^2[/tex] + 18x + 3

The general form of the quadratic function is

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

If a < 0, the quadratic function has maximum value

Here the value of a = -3

Therefore the function has maximum value.

Maximum value will be at x = -b / 2a

= -18 / 2(-3)

= -18 / -6

= 3

The maximum value of quadratic function will be (4ac - [tex]b^2[/tex]) /4a

Substitute the value in the equation

(4ac - [tex]b^2[/tex]) /4a = (4×-3×3 - 18×18) / 4×-3

= (-36 - 324 / -12

= -360 / -12

= 30

Hence, the function f(x) = [tex]-3x^2[/tex] + 18x + 3 has the maximum value of 30 at x = 3

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If a line's angle with the x-axis is then, that line's slope will be tanα, and the new road's slope will be tan(0) = 0.

D Street is depicted as a vertical line with a 90° angle of inclination in the accompanying figure. In other words, D Street has an infinite slope.

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

A horizontal line now has zero slopes.

The new road has a zero slope as a result.

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Answer:

178 000

Step-by-step explanation:

178 383      8 is in the thousands place...if the number next to it (3) is ≥ 5 round it up by 1   o/w leave it alone

Answer:

178,000

Step-by-step explanation:

It's 178,000 because the number in front of the 8 in 178,383 was under five so the number dropped.

Answer: 4x + 29

Step-by-step explanation: add the like terms together.

Answer:

39 inches

Step-by-step explanation:

the triangle has all equal angles

this means it is equilateral and this also means all the sides are equal

so take 2 sides and set them equal to each other to find x

21 - x = x + 5

now solve

add x to both sides

21 = 2x + 5

subtract 5 to both sides

16 = 2x

divide everything by 2

8 = x

now flip it

x = 8

plug this is to one of the equations and multiply that by 3

8 + 5 = 13

13 * 3 = 39

that is the perimeter

The distance between points  (-3,-4) and (2,8) is 13.

A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees, or it follows Pythagoreans theorem.

The horizontal distance = 5

And the vertical distance = 12

The vertical and horizontal lines make a right angle when they meet,

To find distance between points, use Pythagoreans theorem,

(D)² = (5)²+(12)²

(D)² = 25 + 144

(D)² = 169

D = 13

The distance between points  (-3,-4) and (2,8) is 13.

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Answer:

gradient:

y2-y1/x2-x1

1-1/9-3

0/-6

= 0

Using Simplification , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14)  are (6x+2)/3 = -3x - 12 and  6x + 2 = -9x - 36 , the correct option is  (a) and (d) .

In the question ,

it is given that

the equation is (6x+2)/3 = 2 - (3x+14)

solving the brackets on the right side of the equation ,

(6x+2)/3 = 2 - 3x - 14

(6x+2)/3 = -3x - 12                     ....option(a)

On Cross Multiplying , we get

6x + 2 = 3(-3x - 12)

6x + 2 = -9x - 36                      ....option(d)

Therefore , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14)  are (6x+2)/3 = -3x - 12 and  6x + 2 = -9x - 36  .

The given question is incomplete , the complete question is

Using Simplification , Select all equations that are equivalent to

(6x+2)/3 = 2 - (3x+14)

(a) (6x+2)/3 = -3x-12

(b) (6x+2) = 2 - (3x+14)

(c) 2x + 2/3 = 2 - (3x+14)

(d) 6x+2 = -9x-36

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The annual percentage rate of depreciation of the number of rhinos represented by the statistics is approximately 6.41 %

The rate of depreciation is the rate at which the number or value of an item reduces within each specified period.

The initial number of black rhinos in 1970 = 60,500

The number of black rhinos remaining in 2011 = 4,000

The annual rate of depreciation can be found using the formula;

Where;

FV = The future value = 4,000

PV = The present value = 60,500

r = The annual depreciation rate

n = The number of years

[tex]4,000 = 60,500 \times \left(1+\dfrac{r}{100} \right)^{(2011-1970)}=60,500 \times \left(1+\dfrac{r}{100} \right)^{41}[/tex]

[tex]\left(1+\dfrac{r}{100} \right)^{41} = \dfrac{4000}{60500} = \dfrac{8}{121}[/tex]

[tex]r = 100\times \left(\sqrt[41]{ \dfrac{8}{121}} - 1\right) \approx -6.41[/tex]

The annual rate of depreciation is approximately 6.41%

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The ratio of frames to honey is the same as in a smaller beehive. 200 pounds of honey can be found in Bert's new beehive.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given data:

Number of frame beehives = 6

Pound of honey = 40

Current Frame beehive = 30

The first step is to formulate an equation and then use the formulated equation to find  the number of honey

E = 40 × 30 ÷ 6

E = 40 × 5

E = 200 honey

Therefore the number of honey is 200.

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A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a prospective study.

Individuals are tracked over time in prospective studies, and information is gathered about them as their characteristics or circumstances change. Prospective studies include things like birth cohort studies. In retrospective research, people are sampled, and details about their past are gathered. Always after a predetermined number of incidents, the analysis takes place. The fact that individuals were enrolled and baseline data was obtained before any subjects experienced an outcome of interest identifies a study as prospective.

Given,

A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a ...

Prospective study

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The factored form of f(x) = x³ + 8x² - 23x - 30 is (x - 3)(x + 10)(x + 1).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given a polynomial f(x) = x³ + 8x² - 23x - 30.

If f(3) = 0 then x - 3 is one of the factors of the polynomial f(x).

∴ f(x) = f₁(x)(x - 3), where f₁(x) is a quadratic equation we obtain it by long division or synthetic division.

f₁(x) = x² + 11x + 10.

Now, x² + 11x + 10 = 0.

x² + 10x + x + 10 = 0.

x(x +10) + 1(x + 10) = 0.

(x + 10)(x + 1) = 0.

x + 10 = 0 Or x = 1 = 0.

x = - 10 Or x = - 1.

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Answer:

  -1/11, +1/11

Step-by-step explanation:

You want the two square roots of 1/121.

A square root can be either positive or negative.

  [tex]\pm\sqrt{\dfrac{1}{121}}=\pm\dfrac{1}{\sqrt{121}}=\boxed{\pm\dfrac{1}{11}}[/tex]

__

Additional comment

The √ symbol generally means the principal square root, the positive root. To get the negative root, we precede the symbol with a minus sign. So, both square roots are identified as ±√( ).

The answer to the given question is <0.01.

What is confidence level?

The confidence level is the percentage of times we expect to get near to the same approximate if we run our experiment again or resample the population in the same way. The confidence level is the probability that the null hypothesis is true.

What is p-value?

P-value is the probability of getting the results you did, given that the null hypothesis is true.

When we are conducting a hypothesis testing and we determine the confidence level needed is 99%; then in order to reject the null hypothesis, the p-value needs to be below 0.01 (<0.01).

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The simplified form of the given fraction is, 2/3.

What is greatest common factor?

The largest gap between the two integers is considered to be the biggest common factor. Firstly, make a list of each number's prime factors to determine its largest common factor. The ages of 18 and 24 have one 2 and one 3. The GCF of 18 and 24 is obtained by multiplying them, therefore 2 * 3 = 6.

Consider, the given fraction [tex]\frac{48}{72}[/tex]

The divisors of 48 are, 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

The divisors of 72 are, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

So, from above the greatest common factor of 48 and 72 is 24.

Therefore,

[tex]\frac{48}{72} = \frac{24(2)}{24(3)} = \frac{2}{3}[/tex]

Therefore, the simplified form of the given fraction is, 2/3.

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The two positive numbers are 5 , 5.

Given:

Product of two positive numbers = 25

sum of these number is minimum.

Let a and b be the two positive numbers.

a*b = 25

b = 25/a

sum s = a+b

= a + 25/a

apply derivation on both sides.

ds/da = 1 - 25/[tex]a^{2}[/tex]= 0.

1 = 25/[tex]a^{2}[/tex]

a = [tex]\sqrt{25}[/tex]

a = 5 , -5

since given are positive numbers so 5 is considered.

b = 25/5

b = 5

Therefore the two positive numbers are 5 , 5.

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The density of the planet is 4.81 g/cm^3, and with this in mind, we assume that the planet is made of titanium or yttrium.

Density is defined as the quotient between mass and volume.

Here we know that the mass is:

9.43*10²⁷g

And the radius is 7.6x10^8cm, remember that the volume of a sphere of radius R is:

V = 3.14*(3/4)*R³

Then in this case the volume is:

V = 3.14*(3/4)*(9.43*10⁸ cm)³ = 1.96*10²⁷ cm³

Then the density is:

D = (9.43*10²⁷g)/(1.96*10²⁷ cm³) = 4.81 g/cm^3

For this density, we can assume that the planet is made of Titanium or Yttrium (or a combination of a lot of elements like most planets)

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The function whose graph is shifted 2 units to the left is y = (x + 2)² .

In the question ,

it is given that the equation is given as y = x² .

we know that when the function y = x² is shifted " a units " to the left , the shifted function becomes y = (x + a)²  ,

we have to find the equation of the graph that is shifted 2 units to the left ,

So , the value of a is 2 ,

and the equation becomes

y = (x + 2)²

so , the equation is y = (x + 2)² .

the graph is shown below .

Therefore, The function whose graph is shifted 2 units to the left is y = (x + 2)² .

The given question is incomplete , the complete question is

Write the function whose graph is the graph of y = x², but is shifted to the left 2 units ?

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Alexi will not like the drink because the ratio of liquid to ice is 1/1.

Alexi likes her drink to have a liquid-to-ice ratio of about 1/3. A fast food restaurant put 16 ounces of ice in her 32-ounce cup. We need to find out if Alexi will like her drink or not, and if not, why not.

Let the ratio of the liquid to the ice in the drink be represented by the variable "R". The total volume of the cup is 32 ounces. The amount of ice in the cup is 16 ounces. So the amount of liquid in the drink is the difference between these two amounts. Hence, the amount of liquid in the cup is 32 - 16 = 16 ounces.

The ratio of the amount of liquid to the amount of ice in the drink is calculated below.

R = 16/16

R = 1/1

Hence, the ratio of the amount of liquid to the ice in the drink is 1/1. So, Alexi will not like her drink.

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Answer:

Can't be solved

Step-by-step explanation:

Using Pythagoras theorem,

H2= O2 + A2 (where, H= Hypotenuse,O=Opposite,A=Adjacent)

The hypotenuse,H=7feet long

If the opposite side of the triangle is 4 feet longer than the adjacent side, then;

O=A+4

while, A=A

,then using H^2= O^2 + A^2(The 2 are power,that is square)

7^2 = (A+4)^2 + A^2

49= (A+4)(A+4) + A^2

49=A^2 +4A+4A+16 + A^2

49=A^2+8A+16+A^2

(collect like terms)

49-16=A^2+A^2+8A

33=2A^2+8A

Then a quadratic equation,

2A^2+8A=33

2A^2+8A-33=0,

using (-b+/-√4ac) /2a

where b=8, a=2, c=-33

[-8 +/-√4*2*(-33) ]/2(2)

-8 +/-

Answer:

35 square inches

Step-by-step explanation:

21x15=315

315/9=35

Therefore, the answer is 35 square inches

Answer: 25 cents i am sorry if this is wrong

Step-by-step explanation: 3 dimes are 30 cents plus 50 is 80 plus 35 is $1.15 so then when she removers 3 nickles she is getting rid of 15 cents which would leave $1.00 finally when you remove 75 cents you have 25 cents

Answer:

488

Step-by-step explanation:

2(20x8) + 2(20x3)+2(8x3)

Assuming the "x" is not a variable.

The answer is 488

However, if "x" is a variable. The equation would be

40x^8 + 56x^3

Answer:

488

Step-by-step explanation:

using BODMAS

METHOD 1.

[tex]2(20 \times 8) + 2(20 \times 3 + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) = \\ = 320 + 120 + 48 \\ = 448[/tex]

METHOD 2.

[tex]2(20 \times 8) + 2(2 \times 3) + 2(8 \times 3) \\ = 2(160) + 2(60) + 2(24) \\ = 2(160 + 60 + 24) \\ = 2 \times 244 \\ =488[/tex]

Answer: 0

Step-by-step explanation:

Since y is 2, and it’s being multiplied by 4, you have 8 - 8 which =0

Y=2

4(2) - 8

8-8

0

Answer:

0

Step-by-step explanation:

4y - 8

Given that,

y = 2

To find the value of given expression, replace y with 2 and solve the expression.

Let us solve it now.

4y - 8

4 × 2 - 8

8 - 8

0

Answer:

Step-by-step explanation:           The simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

What is an integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

The question is incomplete.

The complete question is attached in the picture, please refer picture.

We have an expression:

Thus, the simplification form of the provided expression is 2y⁴/x⁴ option (A) 2y⁴/x⁴ is correct after applying the integer exponent properties.

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