MATHEMATICS HIGH SCHOOL

Which of these is a simplified form of the equation 7p + 4 = − p + 9 + 2p + 3p? A 13p = 13

B 3p = 5

C 7 = 4
D 11 = 15

Answers

Answer 1
Answer:

Answer:

Option (b) is correct.

3p = 5

Step-by-step explanation:

 Given : equation 7p + 4 = − p + 9 + 2p + 3p

We have to write the simplest form of the equation 7p + 4 = − p + 9 + 2p + 3p and choose the correct from the given options.

Consider the given equation

7p + 4 = − p + 9 + 2p + 3p

Simplify , for p on right side by adding similar terms, we get,

7p + 4 =  9 + 4p

Now subtract 4p both side, we have,

7p - 4p + 4 = 9 + 4p - 4p

Simplify , we have,

3p + 4 = 9

Subtract 4 both side, we have,

3p + 4 - 4 = 9 - 4

Simplify, we have,

3p = 5

Thus, Option (b) is correct.
Answer 2
Answer: i think the answer is B 3p = 5

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Solve for x and y simultaneously x-2y=3. 3x²-5xy-16y=24

Answers

Value of x = 0 or 1 and value of y = (-3)/(2) or -1 for the given quadratic equation.

What is quadratic equation?

" Quadratic equation is defined as the polynomial whose highest degree of the given variable is equals to 2."

According to the question,

Given equations,

x-2y=3

⇒x=3 + 2y                                ____(1)

Quadratic equation,

3x^(2) -5xy-16y=24                 ____(2)

Substitute the value of 'x' from (1) in (2) quadratic equation we get,

3(3+2y)^(2) -5(3+2y)y-16y=24

⇒3(9+12y+4y^(2) )-5y(3+2y) -16y-24=0

⇒27+36y+12y^(2) -15y-10y^(2) -16y-24=0

⇒2y^(2) +5y+3=0

⇒2y^(2) +2y+3y+3=0

⇒2y(y+1)+3(y+1)=0

⇒(2y+3)(y+1)=0

⇒(2y+3)=0 or (y+1)=0

⇒y=(-3)/(2) or y = -1

Substitute in (1) to get the value of 'x' ,

x= 3+ 2((-3)/(2)) or x = 3 + 2 (-1)

⇒  x = 0 or x = 1

Hence, value of x = 0 or 1 and value of y = (-3)/(2) or -1 for the given quadratic equation.

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x-2y=3                        ⇒y=(x-3)/2
3x²-5xy-16y=24

We can suggest this system of equations by substitution method.
y=(x-3)/2

3x²-5x(x-3)/2-16(x-3)/2=24
least common multiple=2
6x²-5x(x-3)-16(x-3)=48
6x²-5x²+15x-16x+48=48
x²-x=0
x(x-1)=0
Now, we solve two equations:
1)x=0    ⇒y=(0-3)/2=-3/2
2)x-1=0
x=1  ⇒y=(1-3)/2=-1



Answer: we can two solutions:
solution1:  x=0; y=-3/2
solution2:  x=1, y=-1

Mark ordered 6 boxes of baseballs that each contained 12 baseballs. Then he bought 7 more baseballs. Finally, he returned 3 baseballs because the seams were split. How would you calculate the total number of baseballs Mark has now?

Answers

Answer:  76 baseballs

Step-by-step explanation:

(boxes of baseballs) 12x6= 72. 72+7=79. 79-3=76. So 76 baseballs. Hope this helps :) Easy Math

Use substitution to determine whether 2 is a zero of the function. f(x)=x^(4)-4x^(3)+2x^(2)-3x+14

Answers

Answer:

x = 2 is a zero of f(x)

Step-by-step explanation:

if x = 2 is a zero of f(x) , then f(2) = 0

given

f(x) = x^(4) - 4x³ + 2x² - 3x + 14 , then

f(2) = 2^(4) - 4(2)³ + 2(2)² - 3(2) + 14

    = 16 - 4(8) + 2(4) - 6 + 14

   = 16 - 32 + 8 - 6 + 14

  = 0

since f(2) = 0 then x = 2 is a zero of f(x)

Final answer:

Using substitution, we can determine whether 2 is a zero of the given function.

Explanation:

To determine whether 2 is a zero of the function f(x)=x^(4)-4x^(3)+2x^(2)-3x+14, we can use substitution. We substitute x = 2 into the function and check if the resulting expression equals zero.

f(2) = (2)^(4)-4(2)^(3)+2(2)^(2)-3(2)+14 = 16-32+8-6+14 = 0

Since the result is zero, we can conclude that 2 is indeed a zero (root) of the function.

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What percent is equivalent to the fraction 37/50?

Answers

Since percent is mostly common as a fraction with a denominator of 100, we'll convert the fraction 37/50 to x/100. To convert 50 to 100, you multiply 50 by 2, so you are also going to multiply 37 by 2, which is 74. Now we have the fraction 74/100, so now since the fraction is over 100, we can convert it to a percentage.

So 74% is equal to the fraction 37/50.

The given fraction is equivalent to a percentage of 74%.

One of the parts of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator is divided by the denominator.

When a fraction of a whole is represented as a number between 0 and 100, it is called a percentage.

To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.

The given fraction is 37/50. In order to calculate the percentage of this fraction, first we need to find the value of this fraction and then multiply the resulting value with 100.

So,

37/50 = 0.74

Multiplying the value with 100,

Percentage of 0.74 = 0.74 x 100 = 74%

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A polygon has 35 diagonals. How many sides does it have?

Answers

d=35\n d=(n(n-3))/(2)\n d=(n(n-3))/(2)\n35=(n(n-3))/(2)\n 70=n^2-3n\n n^2-3n-70=0\n n^2-10n+7n-70=0\n n(n-10)+7(n-10)=0\n (n+7)(n-10)=0\n n=-7 \vee n=10\n\n n=10

What are the domain, range, and asymptote of h(x) = 6x – 4?

Answers

The domain is x = 1, 2, 3, 4, 5...... ∈ R (set of real number).

Range:  (0,∞)

Asymptote: y=0.

What is Domain, Range and Asymptote?

The range of a function is the set of output values for the dependent variable.

The range, however, is bounded by the horizontal asymptote of the graph of f(x).

A straightline that continuously approaches a certain curve without ever meeting it is an asymptote.

Given:

h(x) = 6x – 4

Now, the domain is the input value as

x = 1, 2, 3, 4, 5...... ∈ R (set of real number)

So, h(1) = 6-4 =2

and, h(2) = 12-4 = 8

and, the range is (0,∞)

Now, the asymptote h(x)= 0

6x-4 = 0

x= 2/3.

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h(x)=6x−4  or  h(x)=6x−4 
If the former, the domain is all real numbers, often denoted by the symbol R. 
the range is (0,∞) 
asymptote is y = 0
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