Write the equation of the line in fully simplified slope-intercept form.
2H990 S4321
12
11
10
8
7
6
5
-12-11-10-9-8-7-6-5-4-3-2-1₁ 1 2 3 4 5 6 7 8 9 10 11 12
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
-X

Answer:

  25 yards long, 5 yards wide

Step-by-step explanation:

The given parameters can be used with the area and perimeter formulas for a rectangle to form an equation that can be solved for the dimensions.

The length and width can be represented by x and y. The formulas for area and perimeter give two equations relating these two variables:

  A = LW   ⇒   125 = xy

  P = 2(L+W)   ⇒ 60 = 2(x +y)

Using the second equation to write an expression for y, we have ...

  y = 30 -x

Substituting into the first equation gives ...

  125 = x(30 -x)

This suggests we can find x by looking for factors of 125 that total 30.

  125 = 1(125) = 5(25)

Factor totals are 126 and 30. This means we have ...

  x = 5, y = 30-5 = 25

or

  x = 25, y = 30 -25 = 5

The rectangle dimensions are 5 yards by 25 yards.

__

Additional comment

The two equations can also be solved graphically, as in the attachment.

The rectangle will be 25 yards long, and 5 yards wide.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

The given parameters can be used with the area and perimeter formulas for a rectangle to form an equation that can be solved for the dimensions.

The length and width can be represented by x and y. The formulas for area and perimeter give two equations relating to these two variables:

 A = LW   ⇒   125 = xy

 P = 2(L+W)   ⇒ 60 = 2(x +y)

Using the second equation to write an expression for y, we have ...

y = 30 -x

Substituting into the first equation gives ...

125 = x(30 -x)

This suggests we can find x by looking for factors of 125 that total 30.

125 = 1(125) = 5(25)

Factor totals are 126 and 30. This means we have.

x = 5, y = 30-5 = 25

x = 25, y = 30 -25 = 5

Therefore, the rectangle will be 25 yards long, and 5 yards wide.

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Hello!

miles driven = x

the initial cost = 29

f(x) = 29 + 0.35x

Answer:

We can simplify the expression as follows:

4^3 * 4^4 / 4^9

First, we can simplify the terms in the numerator by adding the exponents of 4:

4^3 * 4^4 = 4^(3+4) = 4^7

Now, we can substitute this value in the expression:

4^7 / 4^9

To divide powers with the same base, we can subtract their exponents:

4^(7-9) = 4^(-2)

Therefore, the simplified expression is:

4^3 * 4^4 / 4^9 = 4^(-2)

So, the final answer is 1/16 or 0.0625.

Answer:

The answer is D.

Step-by-step explanation:

Range of a function is determined by the y-axis.

Domain of a function is determined by the x-axis.

So in this graph, the maximum value of y is 2 and the minimum is -3.

The annual interest rate is 8%

The length of the investment in years is 6 yr.

The periodic interest rate is 2%

The number of periods of the investment periods \(=\frac{24}{\text { periods. }}\)

As per the details share in the above question are as follow,

Given time period of t=5 years

Where the Interest rate of =8 % (Quarterly compounding)

Note: for quarterly compounding n=4

(a) So the annual interest rate will be of 8 %

(b) Further the length of Investment in years 6 years

(C) The Periodic interest rate

\($(\gamma)=\left(\frac{8}{4}\right)=2 \%$\)

(d) Number of periods for investment \($=n t$\)

\(\Rightarrow 4 \times 6=\frac{24}{\text { periods. }}\)

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Answer:

Option B

Step-by-step explanation:

\(PV = nRT\\\rule{150}{0.5}\\\rightarrow \frac{PV = nRT}{nR}\\\\\rightarrow \boxed{\frac{PV}{nR} = T}\)

Hope this helps.

The equation for T will be;

⇒ T = PV/nR

Where, P, V, and T represent pressure, volume, and temperature, n represents the number of moles of gas, and R is a constant for the ideal gas.

Option B is true.

What is Linear equation?

When in an equation the highest power of variable is one then its called Linear equation.

Given that;

The equation for the ideal gas law is,

PV = nRT

Where, P, V, and T represent pressure, volume, and temperature,

n represents the number of moles of gas, and R is a constant for the ideal gas.

Now,

Solve the equation for T as;

PV = nRT

Divide both side by 'nR' we fet;

PV/nR = nRT/nR

PV/nR = T

T = PV/nR

Thus, The equation for T will be;

⇒ T = PV/nR

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The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.

The correct answer is D.

The function f(x) has some specific characteristics as shown in the graph.

The graph of f(x) has five intercepts, as can be seen from the graph.

The intercepts of f(x) can be determined by observing where the graph of f(x) crosses the x-axis.

The function f(x) intercepts the x-axis at five different points: -6 only, -2, -1, 1, and 3 only.

At these points, f(x) = 0.
Furthermore, the graph of f(x) is increasing from -∞ to -6, then decreasing from -6 to -2.

The graph of f(x) then increases from -2 to -1, decreases from -1 to 1, increases from 1 to 3, and finally decreases from 3 to +∞.

Hence, we can deduce that the graph of f(x) has a local maximum point at x = -6, a local minimum point at x = -2, and another local minimum point at x = 3.
We can also conclude that f(x) is an odd function, meaning that f(-x) = -f(x).

This can be deduced from the symmetry of the graph about the origin.

Finally, we can see from the graph that the function f(x) is continuous everywhere except at x = -2 and x = 3.

At these points, f(x) is not defined.
The function f(x) has five intercepts at -6 only, -2, -1, 1, and 3 only.

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By using properties of operations, (1) both expressions are equivalent and (2) both expressions are not equivalent.

What is the property of the equation?

The properties of the relationship of equality, reflexivity, symmetry, transitivity, and the properties of operations are employed to solve an equation. These characteristics hold true in both propositional language and arithmetic.

1) Given, (x + 10) + x + 9 and 2 (x + 7) + 5

So, (x + 10) + x + 9 = (x + x) + (10+9) = 2x + 19

And, 2 (x + 7) + 5 = 2x + 14 + 5 = 2x + 19

Hence, both expressions are equivalent.

2) Given, 0.5x + 1 and 1 (0.5x)

So, 0.5x + 1  = 0.5x + 1

And, 1 (0.5x) = 0.5x

Hence, both expressions are not equivalent.

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Answer:

If Father is four times older than Mary, that would be 4 times 10-- which equals 40. Five years ago, Mary must have been 5 years old. So, multiply 7 and 5 and you'll get 35! Father would have been 35 years old.

I hope this helps!

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula for fundung the nth term of t geometeric series is expressed as;

Tn = ar^(n-1)

a is the first term

n is the number of term

r is the common ratio

Given

a = 3

r = 21/3 = 48/12 = 4

Substitute

Tn = 3(4)^(n-1)

Tn = 3(4^n/4)

Tn = 3/4(4^n)

Tn = 0.75(4^n)

Hence the nth term of the geometric series is Tn = 0.75(4^n)

To get any term, simply substitute the value of into the equation

Quadrilaterals are plane shapes with four sides. Thus, the required answers are:

a) The first shape is a right trapezoid.

b) The second shape is a parallelogram.

The given properties are that of a quadrilateral, thus both shape is a quadrilateral. A quadrilateral is a family of shapes that have four straight sides. Examples include squares, rhombus, kites, etc.

A. Given that the shape has one right angle and parallel sides. Then considering the given properties, the most likely shape is a right trapezoid.

A right trapezoid is a type of trapezium that has one right angle, and a pair of parallel sides. Thus the shape here is a right trapezoid.

Other shapes could be ruled out by comparing their properties with the properties of the shape given in the question.

B. The properties of the required shape as given are: it has two pairs of congruent opposite sides, and 2 pairs of opposite parallel sides. Thus the most likely shape required here is a parallelogram. A parallelogram is a shape with parallel and congruent opposite sides, and no right angle.

Other shapes could be ruled out by comparing their properties with the properties of the shape given in the question.

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Kindly contact a 1-on-1 tutor if more explanations are required.

Answer:

X=60°

Step-by-step explanation:

Because the sum of angle of all side of a triangle is 180°

and

if that goes on

the equation become

x°+75°+45°=180°

x°+120°=180°

x°=180°-120°

x°=60° hence prove

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

2(19x - 1)

Step-by-step explanation:

The GCF of 38 and 8 is 2 :

Now we take a common factor of 2 :

2(19x - 1)

Hope this helped and have a good day

Answer:
2(19x-4)

The gcf of 38 and 8 is 2 so factor it out.

The number used in the blanks to satisfy the inequality is 1/2.

i.e

1/2 x 12 < 12

6 < 12

We have,

___ x 12 < 12

Now,

To fill in the blank we substitute the following.

- 2/2

- 3/2

- 1/2

Substitute each option in the blanks and see which satisfies the inequality.

Now,

2/2 x 12 < 12

1 x 12 < 12

This is not true.

3/2 x 12 < 12

3 x 6 < 12

18 < 12

This is not true.

1/2 x 12 < 12

6 < 12

This is true.

Thus,

The number used in the blanks to satisfy the inequality is 1/2.

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The probability of rolling a 3 first, then an even number, is 1/12.

So, in the given situation the first roll has no effect on the second roll because they are separate events.

Because they are independent, the probabilities of the two events can be multiplied.

Now, we will multiply the two probabilities as follows:

Therefore, the probability of rolling a 3 first, followed by rolling an even number is 1/12.

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Answer:

x = ±5i

General Formulas and Concepts:

Pre-Alg

Alg II

Step-by-step explanation:

Step 1: Define function

k(x) = -5x² - 125

Step 2: Find roots

Answer:

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

  (f(x+h) -f(x))/h = 4h +8x +5

  f'(x) = 8x +5

Step-by-step explanation:

For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.

Put (x+h) where h is in the function, and simplify:

  f(x+h) = 4(x+h)² +5(x+h) +3

  = 4(x² +2xh +h²) +5x +5h +3

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

The difference quotient is ...

  (f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h

  = (4h² +8xh +5h)/h

  (f(x+h) -f(x))/h = 4h +8x +5

When h=0, the value of this is ...

  f'(x) = 4·0 +8x +5

  f'(x) = 8x +5

__

Additional comment

Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.

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Step-by-step explanation:

(2^5)^-5

=2^(-25)

X^5 × X^-5

=X^5-5

=X^0 = 1

(6^5)/(6^-5)

=6^(5-(-5))

=6^10

3(x^2)/3xx

=3x^2/3x^2

=1

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It will help me a lot

If Mira had spent the same total amount of time but an equal amount of time on each problem, each problem would have taken around 2.36 minutes.

In the given plot, Mira spent varying amounts of time on each of the 55 math problems. To find out how many minutes each problem would have taken if Mira had spent an equal amount of time on each problem, we need to calculate the total time she spent and divide it by the number of problems.

Looking at the plot, we can estimate the total time Mira spent by counting the dots above each tick mark and multiplying them by the corresponding time interval. Let's break it down step by step:

The tick marks on the plot are at 7, 7.5, 8, 8.5, 9, 9.5, and 10 minutes per problem.

There are 2 dots above the unlabeled tick mark between 8 and 8.5 minutes per problem. We can assume it represents 8.25 minutes.

There are 3 dots above the 9.5 minutes per problem tick mark.

Now, let's calculate the total time Mira spent:

(7 * 2) + (7.5 * 2) + (8 * 2) + (8.25 * 2) + (9 * 2) + (9.5 * 3) + (10 * 2) = 129.5 minutes.

Since Mira spent a total of 129.5 minutes on 55 problems, each problem would have taken approximately 2.36 minutes (rounded to two decimal places) if she had spent an equal amount of time on each problem.

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Answer:

u > 7

Step-by-step explanation:

-2u -6 < -20  Add 6 to both sides

-2u - 6 + 6 < -20 + 6

-2u < -14  Divide both sides by -2.  When you multiply or divide both sides by a negative number, you must flig the sign.

\(\frac{-2u}{-2}\) > \(\frac{-14}{-2}\)

u > 7

Helping in the name of Jesus.

The answer is:

u > 7

In-depth explanation:

You haven't told me what the values of u are, but I'll solve the equation for u.

Add 6 on each side:

\(\bf{-2u-6 < -20}\)

\(\bf{-2u < -14}\)

Divide each side by -1 and reverse the sign:

\(\bf{2u > 14}\)

Now divide each side by 2

\(\bf{u > 7}\)

Answer:

42 blocks

Step-by-step explanation:

If each block is 2 inches, and the height of the door is 84 inches, you need to divide the height by the block size. Once you divide 84 by 2, you should get 42 blocks as your answer.

the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

Given: The hypotenuse of the right triangle,

c = 159 ft; angle A = 34°

We know that, in a right-angled triangle:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$\)

We know the value of the hypotenuse and angle A. Using trigonometric ratios, we can find the length of sides in the right triangle.We will use the following formulas:

\($$\sin\theta=\frac{\text{opposite}}\)

\({\text{hypotenuse}}$$$$\cos\theta=\frac{\text{adjacent}}\)

\({\text{hypotenuse}}$$$$\tan\theta=\frac{\text{opposite}}\)

\({\text{adjacent}}$$\) Length of side a is:

\($$\begin{aligned} \sin A &=\frac{a}{c}\\ a &=c \sin A\\ &= 159\sin 34°\\ &= 91.4 \text{ ft} \end{aligned}$$Length of side b is:$$\begin{aligned} \cos A &=\frac{b}{c}\\ b &=c \cos A\\ &= 159\cos 34°\\ &= 131.5 \text{ ft} \end{aligned}$$\)

Now, we have the values of all sides of the right triangle. We can calculate the area of the triangle by using the formula for the area of a right triangle:

\($$\text{Area} = \frac{1}{2}ab$$\)

Putting the values of a and b:

\($$\begin{aligned} \text{Area} &=\frac{1}{2}ab\\ &=\frac{1}{2}(91.4)(131.5)\\ &= 6006.55 \approx 6007 \text{ sq ft}\end{aligned}$$\)

Therefore, the length of side a is 91 ft (rounded to the nearest whole foot) and the length of side b is 132 ft (rounded to the nearest whole foot). The area of the triangle is approximately 6007 sq ft.

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Answer:

The retained earnings decreased by $1,020,600

Step-by-step explanation:

Given that Rayan Company has 420,000 shares of $ 10 par. Rayan then declared a 5% share dividend when the market price of the shares was $36 per share.

Let's calculate the shares issued as stock dividends below:

Issued shares = stock dividends * outstanding shares

= 5% * 420,000

= 21,000

21,000 shares were issued.

Let's calculate the stock dividends.

Stock dividends = issued shares * market price per share

= 21,000 * $36

= $756,000

Stock dividends is $756,000

Let's calculate the amount of cash dividends, since the company declared a $0.60 per share cash dividend after 3 months. We have:

Cash dividend = cash dividend per share * new number of shares.

= $0.60 * (420,000 + 21,000)

= $0.60 * 441,000

= $264,600

Cash dividends paid is $264,600

The find the decrease in retained earnings, we have:

Decrease in Retained earnings = cost of stock dividend + cash dividend.

= $756,000 + $264,600

= $1,020,600

Therefore, the retained earnings decreased by $1,020,600

In the given inequality 14 + x > 5, the graph represents the value of x greater than -9.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

When the inequality is plotted on the graph it represents that the value of x is greater than -9.

The graph of the inequality  14 + x > 5, is attached with the answer below.

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The simplified value of the expression ((2⁵ x 5²² - 2 x 5²¹) / 25¹⁰ is 790.

To simplify the expression (2⁵ x 5²² - 2 x 5²¹) / 25¹⁰.

we can use the properties of exponents and the fact that 25 = 5².

First, let's simplify the numerator:

(2⁵ x 5²² - 2 x 5²¹)

Using the distributive property, we can factor out 5²¹ from both terms:

= 5²¹ x (2⁵ x 5 -2)

= 5²¹ (32 x 5- 2)

= 5²¹ (160-2)

= 5²¹ x 158

Now, let's simplify the denominator: 25¹⁰

Since 25 = 5², we can rewrite it as (5²)¹⁰, which gives us:

=  (5²)¹⁰

= 5²⁰

Using the quotient rule of exponents \((a^m / a^n = a^{(m-n)})\), we can simplify further:

=  5²¹ x 158 / 5²⁰

= 5²¹⁻²⁰ x 158

= 5 x 158

= 790

Therefore, the simplified value of the expression ((2⁵ x 5²² - 2 x 5²¹) / 25¹⁰ is 790.

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There will be 25 sample outcomes that are possible when two five sided dices are rolled.

Teo five sided dice rolled in this experiment, The sample space can be defined as:

n = (1,1) (1,2) (1,3) (1,4) (1,5)

(2,1) (2,2) (2,3) (2,4) (2,5)

(3,1) (3,2) (3,3) (3,4) (3,5)

(4,1) (4,2) (4,3) (4,4) (4,5)

(5,1) (5,2) (5,3) (5,4) (5,5)

n = 25

The sample space is defined as the event A is the sum of two dices is six :

n(A) = (1,5) (2,4) (3,3) (4,2) (5,1) = 5

The first die can land face-up in any one of n1 = 5 ways. For each of these 5 ways, the second die can also land face-up in n2 = 5 ways. Therefore, the pair of dice can land in n1n2 = (5)(5) = 25 possible ways.

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The measurement closest to the area of the circle in meters is 379.94 sq. meters.

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The word "area" refers to a free space. A shape's length and width are used to compute its area. The majority of forms and things have corners and edges. When computing the area of a certain form, both the length and width of these edges are taken into account.

Given that,

diameter = 22m

radius = 22/2 = 11m

The area of the circle is:

A = πr²

Substituting the value of π = 3.14 and r = 11 we have:

A = (3.14)(11)²

A = 379.94

Hence, the measurement closest to the area of the circle in meters is 379.94 sq. meters.

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Answer:

∠ x = 58°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠  BAD is an exterior angle of the triangle , then

x + 56° = 114° ( subtract 56° from both sides )

x = 58°