Select the inequality below that could have 7 as a solution.


21x ≥ 7


12+ x > 15


14x 28

f(-5) = 15 (A)

f(x) = - 2x + 5

replace x = - 5

f(-5) = -2(-5) + 5

(-)(-) = +

f(-5) = 10 + 5

f(-5) = 15 (A)

f(-5) = -2(-5) + 5

(-)(-) = +

f(-5) = 10 + 5

f(-5) = 15 (A)

Given:

A farm was 10 miles wide and 7 miles long.

Answer:

it's the 3rd one from the top

Answer:

y + 2 = \(-\frac{3}{2}\) (x - 3)

Step-by-step explanation:

y - \(y_{1}\) = m(x - \(x_{1}\))

If AB ⊥ CD , then \(m_{AB}\) × \(m_{CD}\) = - 1

y + 2 = \(-\frac{3}{2}\) (x - 3)

The graph of the function y = 1/3x - 2 is added as an attachment

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

So, the equation is

y = 1/3x - 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking note of the above transformations rules

The graph of the function is added as an attachment

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Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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When w = 10 and z = 2, the value of expression 2w⁻²z⁰ is equal to 1/50. So, correct option is A.

The expression 2w⁻²z⁰ can be simplified as follows:

2w⁻²z⁰ = 2/w² * z⁰

Since z⁰ = 1 for any non-zero value of z, we can simplify further:

2w⁻²z⁰ = 2/w² * 1

Now we can substitute w = 10 into the expression:

2(10)⁻² * 1 = 2/100 = 1/50

In general, when we have a negative exponent in an expression, we can rewrite it as a positive exponent in the denominator. In this case, w⁻² can be rewritten as 1/w². Additionally, any number raised to the power of 0 is always 1, so z⁰ = 1. By simplifying the expression, we can easily substitute the given values of w and z to evaluate the expression.

So, correct option is A.

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Answer:

13

Step-by-step explanation:

pythagorean theorm calculator

enter the values for each leg

Answer:

x = 8

Step-by-step explanation:

step 1 : 83 + 12x + 1 = 180

step 2 : 12x + 84 = 180 ( subtract 84 from both sides )

step 3 : 12x = 96 ( divide both sides by 12 )

step 4 : x = 8

Sara need 9/4 ounces of chopped nuts

Sara wants to make dinner for herself
The recipe she will use calls for 13 1/2 ounces

The recipe feeds 6 people

The number of ounces of chopped nuts that Sara needs can be calculated as follows

13 1/2

= 27/2 ÷ 6

= 27/2 × 1/6

= 27/12

= 9/4

Hence Sara needs 9/4 ounces of chopped nuts for one serving

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Answer:

33.75

Step-by-step explanation:

Brainiest?

Answer:

The answer is D AC because that line is opposite of angle B

Answer:

1.8

hope this is right

Using the Pythagorean Theorem, it is found that the lot has an area of about 35 acres.

The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle with the length of the hypotenuse h, according to the following equation:

\(h^2 = l_1^2 + l_2^2\)

Researching the problem on the internet, the lot has one leg of 800 feet and the hypotenuse is of 3900 feet, hence the other leg is found as follows:

\(800^2 + l^2 = 3900^2\)

\(l = \sqrt{3900^2 - 800^2}\)

l = 3817 feet.

The area of a right triangle is given by half the multiplication of it's legs. Hence, the area of the lot, in square feet, is given by:

A = 0.5 x 800 x 3817 = 1,526,800 square feet.

Each square feet is equivalent to 0.000029568 acres, hence the area in acres is given by:

Aa = 0.000029568 x 1,526,800 = 35 acres.

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Answer:

8

Step-by-step explanation:

=(7−(−1))2+(4−4)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√

=(8)2+(0)2‾‾‾‾‾‾‾‾‾‾√

=64+0‾‾‾‾‾‾√

=6‾√4

=8

The solution in this case is x = (4 + sqrt(102+4c))/2 - 4√c, which can be expressed in the form of X = a - b√c.

How to solve quadratic equation?

To solve the equation x²+8x-38=0, we can use the quadratic formula:

x = (-b ± sqrt(b²-4ac)) / 2a

Here, a=1, b=8, and c=-38. Substituting these values into the formula gives:

x = (-8 ± sqrt(8²-4(1)(-38))) / 2(1)

x = (-8 ± sqrt(324)) / 2

x = (-8 ± 18) / 2

So x is either -13 or 5.

To find the values of x in the form of X = a + b√c and X = a - b√c, we can use the following steps:

For X=a+b√c:

Let's assume that x = a + b√c, where a, b, and c are constants to be determined.

Substituting this into the original equation x²+8x-38=0, we get:

(a + b√c)² + 8(a + b√c) - 38 = 0

Expanding the square and simplifying, we get:

(a² + 2ab√c + b²c) + 8a + 8b√c - 38 = 0

Separating the real and imaginary parts, we get:

(a² + b²c + 8a - 38) + (2ab√c + 8b)√c = 0

Since the real and imaginary parts of the equation must both be zero, we can set them each equal to zero and solve for a, b, and c.

First, setting the real part equal to zero gives:

a² + b²c + 8a - 38 = 0

This is a quadratic equation in a, so we can use the quadratic formula:

a = (-8 ± sqrt(8²-4(bc-38))) / 2

Simplifying this gives:

a = -4 ± sqrt(4+b(b-10))

Now, setting the imaginary part equal to zero gives:

2ab + 8b = 0

Solving for b, we get:

b = 0 or b = -4

If b = 0, then a² + b²c + 8a - 38 = a² + 8a - 38 = 0, which has roots a = -5 and a = 3. Therefore, the solution in this case is x = -5 or x = 3, which cannot be expressed in the form of X = a + b√c.

If b = -4, then a² + b²c + 8a - 38 = a² + 16c + 8a - 38 = 0. Plugging this into the quadratic formula for a, we get:

a = -4 ± sqrt(102-4c)/2

Therefore, the solution in this case is x = (-4 + sqrt(102-4c))/2 - 4√c, which can be expressed in the form of X = a + b√c.

For X=a-b√c:

Using the same logic, we can assume that x = a - b√c, where a, b, and c are constants to be determined.

Substituting this into the original equation x²+8x-38=0, we get:

(a - b√c)² + 8(a - b√c) - 38 = 0

Expanding the square and simplifying, we get:

(a² + b²c - 8a - 38) + (-2ab√c - 8b)√c = 0

Since the real and imaginary parts of the equation must both be zero, we can set them each equal to zero and solve for a, b, and c.

Setting the real part equal to zero gives:

a² + b²c - 8a - 38 = 0

This is a quadratic equation in a, so we can use the quadratic formula:

a = (8 ± sqrt(8²+4(bc+38))) / 2

Simplifying this gives:

a = 4 ± sqrt(4+b(b+10))

Setting the imaginary part equal to zero gives:

-2ab - 8b = 0

Solving for b, we get:

b = 0 or b = -4

If b = 0, then a² + b²c - 8a - 38 = a² - 8a - 38 = 0, which has roots a = -3 and a = 11. Therefore, the solution in this case is x = -3 or x = 11, which cannot be expressed in the form of X = a - b√c.

If b = -4, then a² + b²c - 8a - 38 = a² + 16c - 8a - 38 = 0. Plugging this into the quadratic formula for a, we get:

a = 4 ± sqrt(102+4c)/2

Therefore, the solution in this case is x = (4 + sqrt(102+4c))/2 - 4√c, which can be expressed in the form of X = a - b√c.

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A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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(a) f(x) =  \(log_2(x)\) is a logarithmic function

(b) g(x) = ∜x is a root function

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2

(e) v(t) = \(5^t\)is an exponential function

(f) w(θ) = sin θ \(cos^{2}\theta\) is a trigonometric function.

(a) f(x) = \(log_2(x)\) is a logarithmic function. Logarithmic functions have the logarithm of the independent variable as the output. Here, the logarithm base is 2.

(b) g(x) = ∜x is a root function. Root functions have the square root or higher roots of the independent variable as the output. Here, the root is a cube root.

(c) h(x) = \(2x^3/(1 - x^2)\) is a rational function. Rational functions are functions that are expressed as the quotient of two polynomials. Here, the numerator is a cubic polynomial and the denominator is a quadratic polynomial.

(d) u(t) = 1 - 1.1t + \(2.54t^2\) is a polynomial of degree 2. Polynomials are functions that are expressed as a sum of powers of the independent variable, with coefficients. The degree of a polynomial is the highest power of the independent variable.

(e) v(t) = \(5^t\) is an exponential function. Exponential functions have the independent variable as the exponent. Here, the base is 5.

(f) w(θ) = sin θ \(cos^{2}\theta\) is an algebraic function and a trigonometric function. Algebraic functions are functions that can be expressed using arithmetic operations and algebraic expressions. Trigonometric functions are functions that involve the ratios of the sides of a right triangle. Here, the function is a combination of sine and cosine functions.

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The complete question is -

Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function.

(a) f(x) =  \(log_2(x)\)    

(b) g(x) = ∜x    

(c) h(x) = \(2x^3/(1 - x^2)\)    

(d) u(t) = 1 - 1.1t + \(2.54t^2\)                    

(e) v(t) = \(5^t\)    

(f) w(θ) = sin θ \(cos^{2}\theta\)

\(\text{We need to find how many pages she can edit in 1 hour}\\\\\text{We know that she can average 160 edits in 8 hours}\\\\\text{With this data, we can find the unit rate}\\\\\text{To get the unit rate, we would divide 160 by 8. This will get us the pages}\\\text{per hour}\\\\160\div8=20\\\\\text{She can edit 20 pages per hour}\\\\\boxed{\text{20 pages}}\)

Answer:

(67, 81)

Step-by-step explanation:

Given that :

Five number summary of scores :

55, 67, 73, 81, 98

Five number summary :

Minimum = 55

Lower quartile = 67

Median = 73

Upper quartile = 81

Maximum = 98

Interval which represents the middle 50% of the grade distribution is the interquartile range, which is the difference between the upper and lower quartile

Hence the interval is ;

Q1, Q3

Q1 = 67 ; Q3 = 81

(67, 81)

Answer:

2!

Step-by-step explanation:

There's 12 eggs in a carton, 5v3 is 2! :)

The given form to expand is (2x-4)^7

and we need to find the coefficient of x^3.

The binomial formula is

where n is a positive integer and a, b are real numbers, and 0 < r ≤ n

Substituting the values a = 2x, b = -4, n = 7 and r = 4

Then we have,

Now the coefficient of x^3 will be

Hence, the coefficient will be 71680.

Electricity

Water supply

Rent

Answer:

Telephone

Internet

gas

Answer:

it is

Step-by-step explanation:

yes, it is. every function is a relation

x²+y-15=10

y=25-x²

Answer:

Step-by-step explanation:

A

-9/4 +9/4 =0

Answer:

17 years old.

Step-by-step explanation:

5 years than 3 times can be represented as 5*3.

5*3=15.

If Eva is 2, and Bill is 15 years older, 2+15=17.

Therefore, Bill is 17 years of age.

The system of linear inequalities is:

The

The solution to the system of the inequalities is the area where the shadings of the two inequalities overlap

Answer:

x > -3

Step-by-step explanation:

4 - 4x < 16

- 4x < 16 - 4

- 4x < 12 (note that both can be divided by -4)

x > -3

That's the final answer.

AND if you're co fused about why the sign changed, you should always remember this

By negative num I mean any number that starts with a minus for example -2, -3, -5, -100

Given that: y = x + 7

y = 4

y = x + 7

y = 4

substitute the value of y into the above question

4 = x + 7

Isolate x

x = 4 - 7

x = - 3

For the second question

y = x + 5 ------ equation 1

y = 3x ----------equation 2

Substitute the value of y = 3x into the equation 1

3x = x + 5

Collect the like terms

3x - x = 5

2x = 5

Divide both sides by 2

2x/2 = 5/2

x = 5/2

substitute the value of x = 5/2 into the equation 2

y = 3x

y = 3 (5/2)

y = 3 x 5 / 2

y = 15/2