Apply the square root principle to solve (x – 2)^2 + 20 = 0.
Question 1 options:

A)

x = 2 + 2i , x = 2 – 2i

B)

x = –2 + 2i , x = –2 – 2i

C)

x = 2 + 2 , x = 2 – 2

D)

x = –2 + 2, x = –2 – 2

9514 1404 393

Answer:

Step-by-step explanation:

We assume your formula is intended to be ...

  p(t) = 17.6(1.25^t)

__

For t=0, ...

  p(0) = 17.6

For t=10, ...

  p(10) = 17.6·1.25^10 ≈ 163.91

For t=25, ...

  p(25) = 17.6·1.25^25 ≈ 4,658.68

Answer:

Perimeter = 32.3

Area = 95.24

Step-by-step explanation:

Given:

△ABC, m∠A=60°

m∠C=45°, AB = 9

To find:

Perimeter of △ABC

Area of △ABC

Solution:

Using angle sum property in a triangle:

m∠A + m∠B + m∠C = 180°

m∠B = 180° - 45° - 60° = 75°

As per Sine Rule:

\(\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}\)

Where  

\(a\) is the side opposite to \(\angle A\)

\(b\) is the side opposite to \(\angle B\)

\(c\) is the side opposite to \(\angle C\)

\(\dfrac{BC}{sin60^\circ} = \dfrac{AC}{sin 75^\circ} = \dfrac{AB}{sin 45^\circ} \\\Rightarrow \dfrac{BC}{\frac{\sqrt3}{2}} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow BC = 12.73\times 0.87 \\\Rightarrow BC = 11.08\)

\(\Rightarrow \dfrac{AC}{0.96} = \dfrac{9}{\frac{1}{\sqrt2}} \\\Rightarrow AC = 12.73\times 0.96 \\\Rightarrow AC = 12.22\)

Perimeter of △ABC = AB + BC + AC = 9 + 11.08 + 12.22 = 32.3

Area of a triangle is given as:

\(\dfrac{1}2\times ab sin(angle\ between\ a\ and\ b)\)

\(\Rightarrow \dfrac{1}{2}\times AB\times AC\times sinA\\\Rightarrow 9\times 12.22\times sin 60\\\Rightarrow \bold{95.24}\)

Answer:

Each boxed lunch costs $11.20

Step-by-step explanation:

29 boxed lunches = $324.80

divide by 29 on each one

1 boxed lunch = $11.20

The unit cost of each boxed lunch would be; 11.20 dollars.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

Given that company orders 29 boxed lunches from a deli for $324.80. If each boxed lunch costs the same amount, then;

29 boxed lunches = $324.80

Now divide by 29 on each one to get the unit cost;

1 boxed lunch = $11.20

Each boxed lunch costs = $11.20

Hence, the unit cost of each boxed lunch would be; 11.20 dollars.

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Answer:

656×1000

Step-by-step explanation:

Answer: 7: 29 stickers for each friend

8: 412 seats in each section

Step-by-step explanation:

We will have to divide 145 (stickers) by 5 (friends) to get 29

We will have to divide 2472 by 6 to get 412

7.) 145 ÷ 5 = 29 → Each friend will get 29 stickers

8.) 2,472 ÷ 6 = 412 → There are 412 seats in each second.

I divided for both problems using the long division method and multiplied which is the inverse operation, to check my work.

Since the y-intercept of the line is (0,1) and the line passes through the point (2,4) which is also satisfied by the equation of the line, the given equation represents the graph of the line.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

The given equation of the line is y = (3/2)x + 1.

To find the y-intercept of the line, substitute x = 0 into the given equation,

y = (3/2)(0) + 1

y = 1

Note that the y-intercept of the graph of the line is also 1.

The graph of the line passes through points (2,4).

To verify whether the equation satisfies the coordinates of (2,4) or not, substitute the coordinates of the point into the given equation:

4 = (3/2)(2) + 1

4 =4

The equation is true.

Hence, it can be said that the given equation represents the graph of the line.

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Answer:

8 tickets

Step-by-step explanation:

Take the total cost and divide by the cost of one ticket to get the number of tickets purchased

66 / 8.25

8

Answer:

choice 3

Step-by-step explanation:

Answer:

Fourth Option

Step-by-step explanation:

The perimeter of a shape is all sides added. So, if you do 2x + 2x + (x+1) + (x+1), you would get 6x+2. To get the answer to the question, you verify to see which one of the options equal to 6x+2.

First option:

2x(x+1) and 2(2x) + 2(x+1). You find what this equals. 2x(x+1) = 2x^2+2x so we can automatically elimate this one.

Second option:

2x(x+1) and 2x+2x+2x+1. Here again you see 2x(x+1) which equals 2x^2+2x and is not correct so we eliminate this.

Third option:

4x(2x+2) and 2x(x+1) + 2x(x+1). Once more you see 2x(x+1) but added to 2x(x+1) which would basically equal 2x^2+2x *2. Therefore, it's not this one.

Fourth option:

6x+2 and 2x+(x+ 1) +2x + (x+ 1). Now this one looks right because we already got 6x+2 and this is the only option that presents that but also because we initially solved 2x + 2x + (x+1) + (x+1) and this equals 2x+(x+ 1) +2x + (x+ 1).

I guess you don't really have to solve each of them you can kinda see and tell that the last one seems right but if you're not sure you should use the process above.

I hope this helped!

Answer:

For the part that contains organic matter your answer is, 35 negative result

For the part that does not contain organic matter your answer is, 60 positive result

Step-by-step explanation:

If we pay attention to the part that contains organic matter the total amount 700 and 665 is positive, so subtract them 700-665 to get 35 negative result

For the part that does not contain organic matter the total amount is 300, and 240 of it is negative, so subtract 240 from 300 to get 60 positive result

Your Welcome, Hope This Helps, And Have an Awesome Day!!!

Answer:

The volume of the oil slick at time t is 6000 * t liters

The area of the oil slick is the proportion of this volume to the thickness of the oil slick.

V = πr^2h

h = 8/10 = 4/5

so

V = πr^2 * 4/5

so

r = sqrt(V5/π4)

R(t) = sqrt(6000t5/π*4)

To find the time t when the oil slick has a radius of 1 kilometer, we need to plug in 1,000 meters for the radius in the above equation and solve for t:

1000 = sqrt(6000t5/π4)

1000000 = 6000t5/π4

1000000 = 6000t5/π4

1000000π4 = 6000t5

250000π = 6000t

t = 250000π/6000

It will take approximately 40.8 hours for the oil slick to have a radius of 1 kilometer

It will take approximately 40.8 hours for the oil slick to have a radius of 1 kilometer

Step-by-step explanation:

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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The measure of HI based on the given diagram is 70 units.

A triangle mid segment is the line joining the midpoint of any two sides of the triangle which is parallel to the third side and is also half of the length of the third side.

HI = 3x + 5

EF = -3x + 55

So,

HI = 1/2(EF)

3x + 5 = 1/2(-3x + 55)

3x + 5 = (-3x + 55) / 2

cross product

2(3x + 5) = -3x + 55

open parenthesis

6x + 10 = - 3x + 55

6x + 3x = 55 - 10

9x = 45

divide both sides by 9

x = 45/9

x = 5

Therefore, the measure of HI and EF are;

HI = 3x + 5

= 3(5) + 55

= 15 + 55

= 70

EF = -3x + 55

= -3(5) + 55

= -15 + 55

= 40

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Answer:

These two values show the range of maximum and the minimum possible approximation of the amount of atoms in the universe.

10000 of the small universe will fit into the big universe.

Step-by-step explanation:

These values are a representative of the possible number of atoms in the universe. They both give a range of possible numbers, within which the number of atoms in the universe can be assigned a a particular value. The range is used to indicate that the value cannot be be exactly determined to be a particular exact number.

The two numbers given are

10^82, and 10^78

If the the larger number of 10^82 is correct, we'll have

10^82 ÷ 10^78

==> 10^(82 -78) = 10000 of the small universe will fit into the larger universe.

The value of x in the lines is 126 degree

We are given that;

Three parallel line and one intersecting line

Angles= (x-6) and 60

Now,

By supplementary angles property

Angle 1 + Angle 2 = 180 degree

Substituting the values of angles

x-6 + 60 = 180

x + 54 = 180

x = 180-54

x = 126

Therefore by supplementary angles answer will be 126 degree.

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The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)  

When a polynomial is factored, its prime factorization is used to break it down into the product of two or more other polynomials. Polynomials may be easily simplified with the use of factoring.

When a polynomial is factored, its factors are expressed as the polynomial's product. Finding the zeros of the polynomial expression or the values of the variables in the supplied expression are both made possible by factoring polynomials.

Here we have

24x⁶ - 1029y³  

Take 3 as common

=> 3(8x⁶ - 343y³)  

As we know 8 = 2³ and 343 = 7³

=> 3[(2x²)³ - (7y)³]  

From the algebraic identities

Take a = 2x² , b = 7y and apply above formula

=> 3[(2x² - 7x)((2x²)²+(2x²)(7y)+(7y)²)]  

=> 3 [ (2x² - 7x) (4x⁴ +14x²y+49y²)]  

Therefore,

(24x⁶ - 1029y³) = 3 (2x² - 7x) (4x⁴ +14x²y+49y²)  

Therefore,

The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)  

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Answer: i think it's 942,480

Step-by-step explanation:

i just multiplied all of the numbers but i'm probably wrong srry

Answer:

7986m^2

Step-by-step explanation:

140-102=38

area of triangle:

(38*66)/2=1254m^2

area of rectangle:

66*102=6732m^2

total area:

1254+6732=7986m^2

Answer:

\(y - 4 = - 3(x - 2)\)

The values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

A theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.

(25). 2x - 1 = x + 1 {equal tangent segments}

2x - x = 1 + 1 {collect like terms}

x = 2

(26). 2x - 4 = x {equal tangent segments}

2x - x = 4 {collect like terms}

x = 4

Therefore, the values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

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(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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the correct answer is isosceles acute

Answer: 0.771 you are welcome

Answer:

Hi

please mark brainliest ❣️

Thanks

Step-by-step explanation:

10 + x / 3 = 12

Cross multiply

10 + x = 12× 3

10 + x = 36

Collect like terms

x= 36 - 10

x = 26

STEP - BY - STYEP EXPLANATION

Given:

36q = 18

Step 1

Divide both-side of the equation by 36

Step 2

Graph the equation

ANSWER

The y-intercept of a function is the value of y when x = 0, which is represented as the value of b in the slope-intercept equation y = mx + b. b is the y-intercept.

If an equation of graph that represents a function is given in slope-intercept form as y = mx + b, the value of b in the function is the value of the y-intercept of the y-intercept.

The y-intercept of the function is the same as the value of y when the value of x is 0, or the point where the line of the function intercepts the y-axis on a given graph that represents the function.

For example, if we are given the equation of a graph that represents a function as, y = 3x + 4, the y-intercept of the function would be 4.

In summary, the y-intercept of the function is the value of b in the equation of the function that is expressed as y = mx + b in slope-intercept form.

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When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer: ....

Ok done. Thank to me :>

Answer:

∠HIJ = 57

∠IJH = 57

∠JHI = 66

Step-by-step explanation:

As a much better answer to the other guy:

You first have to find what the sum of the interior angles are. This can be found using the following expression:

( n - 2 ) × 180

Where 'n' is the number of sides of a polygon. Since this is a triangle:

n = 3

Therefore, the sum the interior angles of a triangle is 180°

Returning to the triangle, it's stated that the triangle is isosceles, meaning the ∠HIJ is the same as the  ∠IJH (the middle point notating the position of the angle.) So then you have 3 angles with the following expressions:

∠HIJ = 5x + 2

∠IJH = 5x + 2

∠JHI = 3x + 33

Since all of the angles need to add up to 180°, we can smush them all into one big equation:

5x + 2 + 5x + 2 + 3x + 33 = 180

If you simplify everything:

13x + 37 = 180

Subtract 37:

13x = 143

Divide by 13:

x = 11

Now that you have x, plug it in to the equations above!

∠HIJ = 5(11) + 2

∠IJH = 5(11) + 2

∠JHI = 3(11) + 33

Simplify.

∠HIJ = 55 + 2

∠IJH = 55 + 2

∠JHI = 33 + 33

Again.

∠HIJ = 57

∠IJH = 57

∠JHI = 66

There you go!