For any nonnegative real number b, (square root of 5)^2 = _

you apply the concept of vertical angles and 180-degree angle

add  43 and 74 to get 117 now subtract it by 180 you get 63 for angle 1

now since angle 1 and 2 are vertical they are both 63

now for angle 3 you add 63 plus 79 is 142 so,  we subtract 142 by 180

therefore, angle 3 is  38 degrees

remember angles cannot be negative at all!

Answer:$2.98

Step-by-step explanation:

The " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

The equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.    

" Eight  further than" implies addition, so we've 8 " The quotient of a number and 7" means dividing a number by 7, so we've x/ 7 " is equal to" means that the expression on the left side is equal to the expression on the right side, so we've =  " 3" is the value to which the expression on the left side is equal, so we've 3  Putting it all together the  judgment " Eight  further than the quotient of a number and 7 is equal to 3" can be  restated into the equation ( x/ 7) =  3  

In this equation, x represents the number we're trying to find. To  break for x, we can manipulate the equation using algebraic operations to  insulate x on one side of the equation.  By abating 8 from both sides of the equation, we get ( x/ 7)- 8 =  3- 8  Simplifying, we have  x/ 7 = -5

To  insulate x, we can multiply both sides of the equation by 7  *( x/ 7) = -5 * 7  This gives us  x = -35  thus, the equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

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Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

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Answer:

The solution is (x, y, z) = (6, 4, 3).

Answer:

9

5

Step-by-step explanation:

Wyatt's class:

Each group of 3 students eats 1 1/2 pizzas.

There are 18 students.

18/3 = 6

There are 6 groups of 3 students.

Since each group of 3 students eats 1 1/2 pizzas, 6 groups eat

6 * 1 1/2 = 6 * 3/2 = 18/2 = 9

Answer: 9 pizzas

Jennifer's class:

There are 15 students. Each student eats 1/3 of a pizza.

15 * 1/3 = 15/3 = 5

Answer: 5 pizzas

Answer:

9

5

Determine the length of side AB.

Determine the length of BC.

Determine the length of CD.

Determine the length of side DA.

All sides of quadilateral are equal. So quadilateral is a square or rhombus with side of 5 units.

Determine the length of diagonal AC and BD.

Diagonals are equal so quadilateral is a square.

Determine the area of square with side 5.

So area is 25 square units.

Answer:

Option (1)

Step-by-step explanation:

Given : m(arc BCD) = 148°

By the property,

Inscribed angle formed by an arc measures half the measure of the arc.

m(arc BCD) = 2(m∠BCD)

148° == 2(m∠BCD)

m(∠BCD) = 74°

Therefore, Option (1) will be the correct option.

Answer:

36° , 54° , 90°

Step-by-step explanation:

since the triangle is right then one angle is 90°

the ratio of the smaller angles = 3 : 2 = 3x : 2x ( x is a multiplier )

the sum of the 3 angles in the triangle is 180° , that is

3x + 2x + 90 = 180

5x + 90 = 180 ( subtract 90 from both sides )

5x = 90 ( divide both sides by 5 )

x = 18

Then

3x = 3 × 18 = 54°

2x = 2 × 18 = 36°

the 3 angles measure 36° , 54° , 90°

In June, A.B.C company invested $20,000, purchased equipment, paid insurance premium, bought office supplies, billed students for tutorial services, received cash, paid for supplies, withdrew personal funds.

Accounting Cycles:

1. June 1:

  - A.B.C company invests $20,000 in the business.

  - Prepare the journal entry:

    - Debit: Cash ($20,000)

    - Credit: Capital ($20,000)

2. June 3:

  - Purchased equipment for $12,100.

  - Prepare the journal entry:

    - Debit: Equipment ($12,100)

    - Credit: Cash ($12,100)

3. June 4:

  - Paid $220 premium for an insurance policy.

  - Prepare the journal entry:

    - Debit: Insurance Expense ($220)

    - Credit: Cash ($220)

4. June 6:

  - Purchased office supplies on account for $140.

  - Prepare the journal entry:

    - Debit: Office Supplies ($140)

    - Credit: Accounts Payable ($140)

5. June 9:

  - Purchased a new computer for $9,000. Paid 40% in cash and agreed to pay the remainder later.

  - Prepare the journal entry for the cash payment:

    - Debit: Computer ($3,600) [40% of $9,000]

    - Credit: Cash ($3,600)

  - Prepare the journal entry for the remaining amount:

    - Debit: Computer ($5,400)

    - Credit: Accounts Payable ($5,400)

6. June 10:

  - Billed student Omar $58 for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Accounts Receivable ($58)

    - Credit: Tutorial Services Revenue ($58)

7. June 14:

  - Paid for the supplies purchased on June 6th ($140).

  - Prepare the journal entry:

    - Debit: Accounts Payable ($140)

    - Credit: Cash ($140)

8. June 15:

  - The owner suggested purchasing a new building for the company for $22,000.

  - No journal entry is required at this point. It is a decision made by the owner.

9. June 25:

  - Received $85 cash from student Salim Ali for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Cash ($85)

    - Credit: Accounts Receivable ($85)

10. June 30:

   - Student billed on June 10 pays the amount due ($58).

   - Prepare the journal entry:

     - Debit: Cash ($58)

     - Credit: Accounts Receivable ($58)

11. June 30:

   - A.B.C company withdraws $60 for personal use.

   - Prepare the journal entry:

     - Debit: Withdrawals ($60)

     - Credit: Cash ($60)

These transactions represent the accounting cycles for the given period.

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Answer: B. y = -8, 4

Step-by-step explanation:

Given expression

y² + 4y - 32 = 0

Cross factorize the expression

y          8

y          -4

Factorize the expression

(y + 8) (y - 4) = 0

Finalize the factor of the expression by the zero product property

\(\boxed{y=-8,4}\)

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Answer:

1/8 per hour

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

The highest grade point is 93 and the lowe

Here we use the Linear Equation concept to calculate the unknown highest and lowest grades. Since we don't know both grade points we represent them with two different variables and will form mathematical expressions as given in the problem.

Solve the equation for the value of variables to get the number of points in given grades.    

Here we have

The highest grade was 14 points higher than the lowest grade.  

Let 'x' be the highest grade and 'y' be the lowest grade

From the given data,

=> x = y + 14 ---- (1)  

Given the sum of the two grade points is 172  

=> x + y = 172 --- (2)

Substitute x = y + 14

=> y + 14 + y = 172

=> 2y + 14 = 172

=> 2y = 158

=> y = 79

Substitute y = 79 in (1)

=>  x = 79 + 14

=>  x = 93

Therefore,

The highest grade point is 93 and the lowest grade point is 79.  

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Answer:

No solutions.

Step-by-step explanation:

Steps:

I will solve your system by substitution.

y=1/4x−10;y=1/4x+1

Step: Solve y=1/4x−10 for y:

Step: Substitute 1/4x−10 for y in y=1/4x+1:

y=1/4x+1

1/4x−10=1/4x+1

1/4x−10+−1/4x=1/4x+1+−1/4x(Add (-1)/4x to both sides)

−10=1

−10+10=1+10(Add 10 to both sides)

0=11

The given system of equation of No solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have the equations:

y= 1/4 x - 10

y = 1/4x + 1

Now, Solve y=1/4x−10 for y by Substituting 1/4x−10 for y in y=1/4x+1 we get

y=1/4x+1

1/4x−10=1/4x+1

1/4x−10+−1/4x=1/4x+1+−1/4x

−10=1

0=11

thus, the equation have No solution.

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Answer:

A

Step-by-step explanation:

X always equals 0 :)

An autonomous differential equation with equilibrium solutions at y=0 and y=3, and y' > 0 for 0 < y < 3 and y' < 0 for -inf < y < 0 and 3 < y < inf is dy/dx = 3y(1-y).

An autonomous differential equation is a type of ordinary differential equation that does not depend on any other variable but time. It has a single variable, usually denoted as y, and a single independent variable, usually denoted as t or x. An autonomous differential equation with equilibrium solutions at y=0 and y=3, and y' > 0 for 0 < y < 3 and y' < 0 for -inf < y < 0 and 3 < y < inf is dy/dx = 3y(1-y). This equation will have two equilibrium solutions at y=0 and y=3. The derivative of the equation, y’, is greater than 0 for 0 < y < 3, which means that the equation is increasing in this range. The derivative of the equation is less than 0 for -inf < y < 0 and 3 < y < inf, which means that the equation is decreasing in this range. This equation is a type of logistic equation and is often used to model population growth. It is also used to describe other phenomena such as the spread of an epidemic or the number of species in an ecosystem. Using the initial conditions y(0) = 2 and y(1) = 3, we can calculate the values of y at other time points using the equation dy/dx = 3y(1-y). At t=0.5, the value of y is y(0.5) = 2.5; at t=1.5, the value of y is y(1.5) = 2.875; and at t=2.5, the value of y is y(2.5) = 2.9375.

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Answer:

x = 81°

Step-by-step explanation:

Refer to the attachment for the steps.~

Answer:

The formula for density (ρ) is:

Density (ρ) = Mass (m) / Volume (V)

Step-by-step explanation:

Where:

The angular motion of the second hand is 720 h , we also have to know the meaning of angular motion.

The body moving along the curved path at a constant angular velocity can be used to describe the angular motion.

As there are 12 hours on a clock, every hour means 360/12 = 30° rotation for the hour hand.

so, for each hour the second hand moves 21600°.

that means 21600/360 = 60 full rotations.

that means one rotation of the second hand is 1 minute.

so, the second hand is truly a second hand (counting the seconds).

60 seconds in a minute (a full rotation by the second hand), that means each second corresponds to 360/60 = 6° rotation of the second hand.

\(the \ ratio \ is\ \frac{30}{21600} = \frac{3}{2160} = \frac{1}{720}\)

that means for every degree the hour hand moves, the second hand does 2 full rotations (2×360°).

h = s×30/21600 = s/720

s = 720 h.

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Answer:

17/8

Step-by-step explanation:

2⅛ as an improper fraction.

2 x 8 = 16

16 + numerator (1) =17.

17/8 is 2⅛ as an improper fraction

Solution:

To convert the fraction into improper fraction, multiply the whole number with the denominator and add the numerator to the product. The denominator will remain the same.

2 1/8 in improper fraction is 17/8.

Using the lowest common factor of the shuttles' run times, they will depart again for the campus simultaneously at 10.25 A.M.

We can use the lowest common factor (LCM) of their run time to determine when they depart again for the campus.

The lowest common factor of 30 and 20 is 60 because both 30 and 20 can divide 60 evenly without a remainder, showing that it takes 60 minutes for the two shuttles to depart for the campus at the same time.

We can conclude that every 60 minutes or hour, the two shuttles simultaneously depart for the campus.  Every hour, the shuttle departing from Ball Hall completes 2 runs, while the shuttle departing from Lot A completes 3 runs.

Thus, using the lowest common factor, the next time both shuttles will depart for the campus at the same time is 10:25 A.M.

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Answer: I believe it would be 2/5.

Step-by-step explanation:

Reduction means the fraction is reduced to it's simplest form.

7/7=1

2/5=2/5

15/13=1 2/13

See as the '2/5' does not change in reduction.

So, '2/5' would be your answer.

Hope this helps! :)

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Answer:

it is 1.05

Step-by-step explanation:

The lightning was 1.7 kilometer away.

In unit time, the distance covered by any object is called speed.

In mathematical term, Speed is express as S=D/T,

where S=speed, D=distance, T= time.

Given that,

The speed of sound = 1225 kilometers per hour

The speed of sound = 340.277 meter/second

Also, the time after thunder heard = 5 seconds

To find distance, use formula distance = speed × time,

Distance = 340.277 × 5

               = 1701.3 meter

               = 1.7 kilometer

The lightning was 1.7 kilometer away.

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Answer:

seven

Step-by-step explanation:

Lol thxx for the points

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Answer:

42

Step-by-step explanation:

5*5+6*3-1

25+6*3-1

25+18-1

43-1

=42

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Answer:

x=2-y

Step-by-step explanation:

subtract y from both sides

x+y-y=z+y

x=2-y