Solve using substitution.
y = –7x − 8
y = 2x + 10

the dimensions of the rectangular garden are 55 ft by 60 ft.

Let's assume that the width of the rectangular garden is x ft. Then, according to the problem, the length is 5 ft longer than the width, which means the length is (x+5) ft.

The area of a rectangle is given by the formula A = length × width. In this case, we know that the area is 3300 ft². So we can set up the following equation:

3300 = x(x+5)

Expanding the right-hand side, we get:

3300 = x²2 + 5x

Now, we can rearrange this equation into a standard quadratic form, by moving all the terms to one side:

x²2 + 5x - 3300 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b²2 - 4ac)) / 2a

where a = 1, b = 5, and c = -3300.

Plugging in these values, we get:

x = (-5 ±√5²2 - 4(1)(-3300))) / 2(1)

x = (-5 ±√(13625)) / 2

x = (-5 ± 115) / 2

We can discard the negative solution, since the width of the garden cannot be negative. Therefore, we have:

x = (-5 + 115) / 2

x = 55

So the width of the garden is 55 ft. And the length is:

x + 5 = 55 + 5 = 60

Therefore, the dimensions of the rectangular garden are 55 ft by 60 ft.

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Answer: 64.2 ft^2

Step-by-step explanation: to find the answer we know that the parallelogram area is A= bh we see that they are trying to trick us by separating the base we have to add the base together and we then get 10.7 that is the base we then see that the height is 6 and we multiply them together and get the answer.

Answer:

1st option

Step-by-step explanation:

Thats a weird problem tho,

-Gage Millar, Algebra 2 tutor

The desired statistical measures are given as follows:

1. The margin of error is of \(M = \frac{6.75}{\sqrt{n}}\).

2. The margin of error is of 0.02 = 2%.

3. The point estimate is of 0.655.

We also have to be given the sample size n, along with the standard deviation s, and the margin of error is given by:

\(M = \frac{s}{\sqrt{n}}\)

In item 1, we have that s = 6.75, hence the margin of error is:

\(M = \frac{6.75}{\sqrt{n}}\)

The margin of error is given by half the subtraction of the bounds, hence, for item 2:

(0.37 - 0.33)/2 = 0.02.

The margin of error is of 0.02 = 2%.

The points estimate is given by the mean of the bounds, hence, for item 3:

M = (0.61 + 0.70)/2 = 0.655.

The point estimate is of 0.655.

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\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-3}~,~\stackrel{y_2}{6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -3 +1}{2}~~~ ,~~~ \cfrac{ 6 +2}{2} \right) \implies \left(\cfrac{ -2 }{2}~~~ ,~~~ \cfrac{ 8 }{2} \right)\implies (-1~~,~~4)\)

Generally, the NEC® permits a fuse to carry 80 percent of its rating when it supplies a load that is not operated continuously. The correct option is b.

According to the National Electrical Code (NEC), a fuse is generally permitted to carry up to 80% of its rating when supplying a load that is not operated continuously. This provision is based on safety considerations and is intended to prevent the fuse from tripping prematurely during temporary or intermittent overloads.

Allowing a fuse to carry up to 80% of its rating ensures that it can handle short-term surges in current without blowing. This is important because many electrical devices and appliances draw higher currents when they are first turned on or during certain operations. Allowing the fuse to handle these temporary overloads helps avoid unnecessary interruptions in power supply.

By limiting the fuse to 80% of its rating, the NEC provides a safety margin. This margin accounts for factors such as variations in load characteristics, ambient temperature, and other operating conditions that may affect the actual current flowing through the fuse.

In summary, the NEC permits a fuse to carry up to 80% of its rating for non-continuous loads to accommodate temporary overloads while maintaining safety and reliability in electrical systems. Hence, b is the correct option.

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Answer: B. 3and 1/6

Step-by-step explanation:

Answer:

(y−10)(y−2)

Step-by-step explanation:

After adding and subtracting the rational expressions , the simplified rational expression is 4x - 4/x² - 5/x³ + 9  .

We first simplify each expression inside the parentheses :

that means :

⇒ (2x + 5/x² -3x) = (2x - 3x + 5/x²) = (-x + 5/x²) ;

⇒ (3x + 5/x³ - 9x) = (-6x + 5/x³)  ;

⇒ (x + 1/x² - 9) = (-9 + x + 1/x²)  ;

Now we substitute these expressions into original equation/expression :

we get ; (-x + 5/x²) - (-6x + 5/x³) - (-9 + x + 1/x²)

Simplifying further ,

we get ;

⇒ -x + 5/x² + 6x - 5/x³ + 9 - x - 1/x²  ;

On Combining the like terms, we get ;

⇒ 4x - 4/x² - 5/x³ + 9

Therefore, the simplified rational expression is 4x - 4/x² - 5/x³ + 9.

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The given question is incomplete , the complete question is

Adding and subtracting rational expressions, Simplify the rational expression  (2x + 5/x² -3x) - (3x + 5/x³ - 9x) - (x + 1/x² - 9)  .

147.5 times 14 = 2065

And they want an estimate so just round the 147.5 to 150.0 and the 14 to a 15 and your answer is 2250

Estimate : 2250

Actual answer is : 2065

If you have any questions comment under this post

Have a wonderful day<3

The correct answer is options 1 and 4: w/x divided by y/z is equivalent to X/w x z/y.

To determine which of the given options is equivalent to w/x divided by y/z, let's simplify each option step by step:

w/x divided by y/z:

(w/x) / (y/z) = (w/x) * (z/y) = wz / xy

X/w x y/z:

(x/w) * (y/z) = xy / wz

X/w x z/y:

(x/w) * (z/y) = xz / wy

W/x x z/y:

(w/x) * (z/y) = wz / xy

X/w divided by z/y:

(x/w) / (z/y) = (x/w) * (y/z) = xy / wz

Comparing the simplified expressions, we can see that options 1 and 4 both simplify to wz / xy, while options 2, 3, and 5 do not.

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Answer: B. 0.058 hectometers

Step-by-step explanation: To convert millimeters to hectometers, you need to divide the number of millimeters by 10,000.

Given that there are 580 millimeters, the conversion to hectometers can be calculated as follows:

580 millimeters ÷ 10,000 = 0.058 hectometers

Answer:

The pattern is:

Step-by-step explanation:

they are the first letters of each month in the year -

J - January

F- Febuary

M - March

A - April

M - May

Continuing...

J - June

J - July

A - August

S - September

O - October

N - November

D - December

Answer: -3

Step-by-step explanation:

6 times 3 is 18, so y is -3

The value of the time premium is $100.

According to the statement

we have to find the time premium from the given information.

So, For this purpose, the given information is:

a strike price of $25 when the option price is $2 and the underlying common stock sells for $24

And

Time premium is the amount by which an option price exceeds its intrinsic value. The value of an option beyond its current exercise value representing the option holder's control until expiration, the risk of the underlying asset, and the risk less return.

So, From the given information and the formula

The value of the time premium is $100.

So, The value of the time premium is $100.

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Answer:

Step-by-step explanation:

Given that:

Initial psi yesterday = 40 psi

psi today = 38 psi

If trend continues and tire loses the same percentage of air. How much air will be left in tire at the end of the week

1 week ( 7days)

Total loss after 7 days = (amount lost per day * number of days)

Total psi lost per day= [(40 - 38) = 2

% psi lost = (2/40) * 100

= 5%

Applying the exponential loss functin:

A = I ( 1 - r)^t

t = 7days ; r = 5% = 0.05 ; A = amount left ; I = Initial amount

A = 40(1 - 0.05)^7

A = 40(0.95)^7

A = 40 * 0.69833729609375

A = 27.933

A = 27.9 psi

B= 1 is the difference between the mean and the median score on this exam.

To begin,

The remaining 30% of students received 95 points.

Assume 20 students are there.

Given,

2 students = 70 points.

5 students = 80 points.

4 students = 85 points

3 students = 90 points

6 students = 95 points

Because the 10th and 11th terms are both 85, the median is 85.

The mean is,

(70 × 2 + 85 × 5 + 85 × 4 + 90 × 3 + 95 × 6) ÷ 20

=  1720 ÷ 20

= 86

As a result, B = 1 for the difference between the mean and median.

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The probability of drawing exactly three face cards is given as follows:

0.0660 = 6.60%.

The mass probability formula is presented as follows:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

Considering that a standard deck is composed of 52 cards, of which 12 are face cards, and 5 cards are taken, the values of the parameters are given as follows:

N = 52, k = 12, n = 5.

The probability of drawing exactly three face cards is P(X = 3), obtained as follows:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 3) = h(3,52,5,12) = \frac{C_{12,3}C_{40,2}}{C_{52,5}} = 0.0660\)

The problem asks for the probability of drawing exactly three face cards.

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Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

To find out how far she will have run in total after 16 days, we can use the formula for calculating compound interest:

A = P(1 + r/100)^n

Where:

A = Total distance run after n days

P = Initial distance (4.8 kilometers)

r = Rate of increase per day (6.9%)

n = Number of days (16)

Plugging in the given values, we can calculate the total distance:

A = 4.8(1 + 6.9/100)^16

Using a calculator or performing the calculations step by step, we get:

A ≈ 4.8(1.069)^16 ≈ 4.8(2.092473)^16 ≈ 4.8(2.628)

A ≈ 12.6144

Rounding to the nearest whole number, she will have run a total distance of 13 kilometers after 16 days.

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Answer:

\(\angle B=150^{\circ}\)

Step-by-step explanation:

The diagram is two parallel lines cut by a transversal therefore Angle A and Angle B are alternate interior angles, in this case meaning they are equivalent (because lines are parallel).

We can use this information to set up an equation:

\(8x-10=3x+90\)

Add 10 to both sides:

\(8x=3x+100\)

Subtract 3x from both sides

\(5x=100\)

Divide both sides by 5

\(x=20\)

Then, substitute 20 for x to solve for Angle B:

\(\angle B=3(20)+90\\\angle B=60+90\\\angle B=150\)

Answer:

B

Step-by-step explanation:

This is because B represents 5/6 times Y which is the amount Kiran earns.

The negative exponent 2⁻⁶ to a positive exponent is 1/64.

A number system is defined as a system of writing to express numbers.

To change a negative exponent to a positive exponent, we can use the following rule:

a⁻ⁿ = 1/(aⁿ)

s power minus n equal to one divided by a to the power of n.

Applying this rule to 2⁻⁶, we get:

2⁻⁶ = 1/(2⁶) = 1/64

Two power minus six equal to one divided by sixty four.

Therefore,2⁻⁶ as a positive exponent is equal to 1/64.

Hence, the negative exponent 2⁻⁶ to a positive exponent is 1/64.

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When the other diagonal is 12 inches long and the side is 10 inches long, the diagonal is 16 inches long.

A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths. A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposing sides of a parallelogram are equal. A quadrilateral with four equal sides that has the shape of a diamond is called a rhombus. In everyday life, rhombus-shaped objects can be seen.

Here,

The length of side=10 inch

The length of diagonal= 12 inch

Let the length of diagonal be x.

6²+(x/2)²=10²

(x/2)²=64

x/2=8

x=16 inch

The length of diagonal is 16 inch when other diagonal measure 12 inch and side measures 10 inch.

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On solving the equation, the total amount that Henry spent on video game and DVD rentals in the past month is $18.30.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

To calculate the total amount Henry spent on video game and DVD rentals, we need to add the cost of renting the video game and the cost of renting the DVDs.

The rental cost of 1 video game is $2.30.

The rental cost equation of 5 DVDs is -

5 DVDs × $3.20/DVD = $16.00

So, the total amount that Henry spent on video game and DVD rentals is -

$2.30 + $16.00 = $18.30

Therefore, Henry spent $18.30 on video game and DVD rentals in the past month.

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Answer:

22/15 in fraction 1 7/15

Step-by-step explanation:

Answer:

___________

Exact Form:

22 / 15

Decimal Form:

1.46 continuous

Mixed Number Form:

1 7/15

To write 9/5 as a fraction with a common denominator, multiply by 3/3

9/5 x 3/3 - 1/3

To write −1/3  as a fraction with a common denominator, multiply by 5/5.

9/5 x 3/3−1/3 x 5/5

Write each expression with a common denominator of 15, by multiplying each by a factor of 1

Multiply 9/5 and 3/3

9 x 3/5 x 3 - 1/3 x 5/5

Multiply 5 by 3

9 x 3/15 − 1/3 x 5/5

Multiply 1/3 and 5/5

9 x 3/15 − 5/3 x 5

Multiply 3 by 5

9 x 3/15 − 5/15

Then combine the numerator over the common denominator

9 x 3 - 5 / 15

then simplify the numerator

mutiply 9 by 3

27 - 5/15

subtract 5 from 27

22/15

Answer:

10

Step-by-step explanation:

First, we know that the angles of a triangle add up to 180 degrees. We can then sum up our angles as 90 (since it's a right triangle, represented by the square in the bottom left angle) +27+6x+3=180

90+27+6x+3=180

Add up left side

120+6x=180

Subtract 120 from both sides

6x=60

Divide both sides by 6

x=10

When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

The value of 6x is 102.

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.

Given:

x=51/3

For 6x put x= 51/3 we get

6x = 6 x 51/3

6x = 2 x 51

6x = 102

Or, \(x^6\) = \((51/3)^6\)

\(x^6\) = 17,596,287,801 / 531,441

Hence, the value of 6x = 102.

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Adding and subtracting polynomials worksheets assist pupils in becoming acquainted with the idea of polynomial addition and subtraction.

Adding and subtracting polynomial worksheets provide pupils with a platform to access a variety of well-structured problems. Because these worksheets progress in complexity, they are simple to use and allow pupils to reinforce their concepts.

Children must study in accordance with their learning curve, and these worksheets are designed to allow young brains to work at their own speed. These math worksheets also address the logical and reasoning aspects of arithmetic, assisting pupils in real-life situations.

Students may have a better grasp and explore these worksheets more quickly with the aid of pictures. These worksheets' step-by-step approach helps pupils better comprehend ideas and reinforce their comprehension.

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