Ken is thinking of a number. nine more than the product of 4 and the number is 73. Find Kens number.

A major baseball diamond is a square with side lengths of 90 feet.

iren2701 [21]

Answer: $\bold{a)\quad 90\sqrt2\qquad \qquad b)\quad 45\sqrt2}$

Step-by-step explanation:

Since you are looking for the distance from home plate to second base, you are actually looking for the length of the diagonal of the square. Use the Pythagorean Theorem: a² + b² = c² where a and b are the side lengths and c is the length of the diagonal.

$90^2+90^2=c^2\\8100+8100=c^2\\16200=c^2\\\sqrt{16200}=c\\\boxed{90\sqrt2}=c\qquad \qquad \text{which is approximately 127.28}\\\\\\\\\text{Halfway between home plate and 2nd base means divide that length by 2:}\\\\\dfrac{90\sqrt2}{2}=\boxed{45\sqrt2}$

7 0

2 years ago

Please explain! Math

Nana76 [90]

I believe (-2,2) or (2,3)

6 0

2 years ago

Solve each of the following systems of equations by substitution

Delvig [45]

Answer:

1) The solution to the given equations is (3,6)

2) The solution to the given equations is (7,-1)

3) The solution to the given equations is (6,5)

Step-by-step explanation:

1) Given equations are $x+y=5\hfill (1)$

and $x=1+y\hfill (2)$

To solve the given equations by substitution method :

From equation (2) we have the value x=1+y

Substitute the value of x=1+y in equation (1) we get

(1+y)+y=5

1+y+y=5

1+2y=5

2y=5-1

2y=4

$y=\frac{4}{2}$

Therefore y=2

Now substitute the value of y=2 in equation (2) we get

x=1+y

x=1+2

Therefore x=3

The solution is (3,6)

2) Given equations are $2x+3y=11\hfill (1)$

and $x+y=6\hfill (2)$

To solve the given equations by substitution method :

From equation (2) we have the value x=6-y

Substitute the value of x=6-y in equation (1) we get

2(6-y)+3y=11

12-2y+3y=11

y=11-12

Therefore y=-1

Now substitute the value of y=-1 in equation (2) we get

x+(-1)=6

x=6+1

Therefore x=7

The solution is (7,-1)

3) Given equations are $x-y=1\hfill (1)$

and $6x-7y=1\hfill (2)$

To solve the given equations by substitution method :

From equation (1) we have the value x=1+y

Substitute the value of x=1+y in equation (2) we get

6(1+y)-7y=1

6+6y-7y=1

-y=1-6

Therefore y=5

Now substitute the value of y=5 in equation (1) we get

x-5=1

x=1+5

Therefore x=6

The solution is (6,5)

8 0

3 years ago

Sketch the graph of the given function. Then state the function’s domain and range. f(x)= 1/2(5)^x+3

balandron [24]

Answer:

Graph of the following function is attached with the answer.

Domain : ( - ∞ , + ∞ )

Range : ( 3 , + ∞ )

Step-by-step explanation:

$f(x)=\frac{1}{2}x^{2}+3$

Domain of any quadratic equation is from negative infinity to positive infinity under no restrictions.

So, Domain : ( - ∞ , + ∞ )

The Range of any function can be calculated easily if there is just one term with variable. The method to find Range by that method is explained with the example as follows:

Range of x : ( - ∞ , + ∞ )
Range of $\textrm{x}^{2}$ : [ 0 , + ∞ ) as every square number is more than or equal to zero.
Range of $\frac{1}{2}\textrm{x}^{2}$ : [ 0 , + ∞ ) as 0/2 = 0 and ∞/2 = ∞.
Range of $\frac{1}{2}\textrm{x}^{2}+3$ : [ 3 , + ∞ ) as 0 + 3 = 3 and ∞ + 3 = ∞.