chris made 4 times as many putts as paul made at golf practice. together they made 60 putts. which equation below canbe used to find the number of putts paul made?
A. 5p=60
B. 4p=60
C. 4+p=60
D. 4p=60+p

The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y.

The value of the equation y = 3x^2 - 18x + 15 can be found by substituting different values of x and calculating the corresponding value of y. For example, if we substitute x = 1, we get y = 3(1)^2 - 18(1) + 15 = 0. So, when x = 1, y is 0.

To find more values, we can create a table of values by substituting different x values into the equation. The resulting values of y can be plotted on a graph to see the pattern and shape of the equation.

Table of Values:

This equation represents a quadratic function in the form of y = ax^2 + bx + c, where a = 3, b = -18, and c = 15.

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Answer:  √3 and √2 are irrational numbers;

                [tex]-\dfracP{1}{16}[/tex] and 0 are rational numbers.

Step-by-step explanation:  We are given to classify the following numbers as rational or irrational:

[tex]\sqrt{3},~~-\dfrac{1}{16},~~0,~~\sqrt{2}.[/tex]

Rational number:   The digits after the decimal are either repeating or terminating.

Irrational number:  The digits after the decimal are non-terminating and non-terminating.

(a) We have

[tex]\sqrt{3}=1.732050807568877~.~.~.[/tex]

Since the digits after the decimal are non-terminating and non-repeating, so √3 is an IRRATIONAL number.

(b) We have

[tex]-\dfrac{1}{16}=-0.0625.[/tex]

Since the digits after the decimal are terminating, so [tex]-\dfrac{1}{16}[/tex] is a RATIONAL number.

(c) We have

[tex]0=0.000.[/tex]

Since the digits after the decimal are  terminating, so [tex]0[/tex] is a RATIONAL number.

(d) We have

[tex]\sqrt{2}=1.414213562373095~.~.~.[/tex]

Since the digits after the decimal are non-terminating and non-repeating, so √2 is an IRRATIONAL number.

The number sentences that solves the problem are;

B. (2 × 16) + (3 × 16) = 80
D. 16 × (2 + 3) = 80

To determine the number sentence, we have from the information given that;

Then, we can say that in each bag, there are;

= 3 + 2
= 5 objects

Now, in 16 of the goodies bag, the number of objects would be;

= 5 ×16

= 80 objects

Therefore, the sentences are in options B and D

Answer: The answer is B) 11.25

Step-by-step explanation: I got it right

The range of the numbers 3, -97, -15, -42 is 100.

The range of a set of numbers is the difference between the largest and smallest numbers in the set. To find the range of the numbers 3, -97, -15, -42, we first need to find the largest and smallest numbers. The largest number is 3 and the smallest number is -97. Subtracting the smallest number from the largest number gives us a range of 100.

Learn more about range here:

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It will take 4 yrs for Rajeev to reach 200$

To find out after how many years Rajeev will have at least $200 in his account, we can use the formula for compound interest. P = $175, A = $200, r = 0.04, n = 1, and t = ? Substituting these values into the formula and solving for t, we find that it will take approximately 7.38 years for Rajeev to have at least $200 in his account.

To find out after how many years Rajeev will have at least $200 in his account, we can use the formula for compound interest, which is given by:

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

Where:

In this case, we have:

Substituting these values into the formula, we get:

$200 = $175(1 + 0.04/1)^(1t)

Simplifying the equation, we have:

1.1429 = (1.04)^t

To solve for t, we can take the logarithm of both sides:

log(1.1429) = log((1.04)^t)

Using logarithmic properties, we have:

t log(1.04) = log(1.1429)

Dividing both sides by log(1.04), we get:

t = log(1.1429)/log(1.04)

Using a calculator, we find that t ≈ 7.38

Therefore, it will take approximately 7.38 years for Rajeev to have at least $200 in his account.

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Final answer:

To find 300% of the difference between 23 and 27, you first calculate the difference, which is 4, and then multiply by 3, giving the result of 12.

Explanation:

The question asks us to calculate 300% of the difference between 23 and 27. First, let's find the difference between these two numbers: 27 - 23 = 4. Now, to find 300% of 4, we multiply 4 by 3 (since 300% is the same as multiplying by 3): 4 imes 3 = 12. Therefore, 300% of the difference between 23 and 27 is 12.This is the final answer.

The exponential function will be written as:

y = 12 (0.56) ^ (t/4)  

y=12 (0.56^ (1/4)) ^t

but

0.56^ (1/4) = 0.8651

thus plugging the value in y we get:

y=12 (0.8651) ^t

in two decimal places we get:

y=12 (0.87) ^t

Option D, which is x + 2y^2 - 7, is a trinomial as it contains exactly three terms.

A trinomial is an algebraic expression with three terms.

These terms are usually separated by '+' or '-' signs. Let's examine the options given to identify a trinomial:

Therefore, Option D is the correct answer as it is the expression that contains exactly three terms, making it a trinomial.

The dimensions are either 4 units by 2 units or 2 units by 4 units.

To draw a rectangle with a perimeter of 12 units and an area of 8 square units, we need to find the dimensions of the rectangle first.

Let  l be the length of the rectangle and w be the width of the rectangle.

We know that the perimeter of a rectangle is given by: P = 2(l + w) =12

12 = 2(l + w) ,6 = l + w

Also, the area of a rectangle is given by: A = l * w = 8

Now, we need to find a pair of numbers  l  and  w  that satisfy both equations:  6 = l + w and  8 = l * w

One such pair is l = 4  and  w = 2 , because ( 4 + 2 = 6 ) and ( 4 * 2 = 8 ).

This rectangle has a length of 4 units and a width of 2 units, with a perimeter of 12 units and an area of 8 square units.

The equation q^2=36 has two solutions because both a positive and a negative number squared can result in a positive number. The solutions are q=6 and q=-6, illustrating the concept of integer powers and square roots.

To solve the equation q squared equals 36 (q2 = 36), we look for the number that, when multiplied by itself, gives the product of 36. In mathematics, finding a value that satisfies this condition involves taking the square root of both sides of the equation. Thus, we have two potential solutions since both positive and negative values can be squared to yield a positive result.

The square root of 36 is 6, so our equation gives us two possible solutions: q = 6 or q = -6. This demonstrates the concept of integer powers, where for instance, raising 4 to the power of 3 (43) means multiplying 4 by itself three times. When dealing with the square root, we are essentially doing the opposite: we are asking what number multiplied by itself gives us the original number under the square power.

Step-by-step explanation:

[tex]-4x-7+10x=-7+6x\\\\(-4x+10x)-7=-7+6x\\\\6x-7=-7+6x\qquad\text{subtract}\ 6x\ \text{from both sides}\\\\-7=-7\qquad\bold{TRUE}\\\\Answer:\ \text{Infinitely many solutions}[/tex]

Final answer:

By simplifying the given linear equation and combining like terms, we find that the single solution is x = 0. Verification confirms that this solution is valid as it satisfies the original equation.

Explanation:

The equation presented by the student is a linear equation with the variables on both sides. To solve this equation, we will combine like terms and isolate the variable x on one side of the equation.

First, let's simplify the equation by combining like terms:

-4x - 7 + 10x = -7 + 6x

Combine x terms on the left side and numerical terms on the right:

6x = 0

Finally, divide by the coefficient of x to solve for x:

x = 0

This value of x is the single solution to the equation. It's important to note that there are no other solutions in this case, as it's a simple linear equation and not a quadratic or higher-order polynomial equation.

Verification

To verify that x = 0 is indeed a solution, we can substitute it back into the original equation:

-4(0) - 7 + 10(0) = -7 + 6(0)

All terms involving x drop out, confirming that -7 = -7 is an identity, making x = 0 a valid solution.

Brand had 2 5/12 cups of chili left over from the second batch (option A). This was determined by solving the equation 1 1/3 + x = 3 3/4 using improper fractions and subtraction.

To find out how many cups of chili were left over from the second batch, we need to solve for x in the equation 1 1/3 + x = 3 3/4. Firstly, convert the mixed numbers to improper fractions: 1 1/3 becomes 4/3 and 3 3/4 becomes 15/4.

Now the equation looks like this: 4/3 + x = 15/4. To find x, subtract 4/3 from both sides of the equation.

15/4 - 4/3 = (15*3 - 4*4)/(4*3) = 45/12 - 16/12 = 29/12.

Now convert the improper fraction back to a mixed number. 29/12 is 2 and 5/12. So Brand had 2 5/12 cups of chili left over from the second batch (option A).