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3 years ago

Lynn can type 1,650 words in 30 minutes. What is her typing rate, in words per minute?

Mathematics

2 answers:

Marianna [84]3 years ago

7 0

55 words per minute

1650/30 = 55

likoan [24]3 years ago

4 0

1650/30

=55

55 words per minute

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What is the volume of this equation?

Pachacha [2.7K]

Answer:

Volume ≈ 33.33 cubic feet

Step-by-step explanation:

The question is:

Find the volume of a right square pyramid with base square edges measuring 5 feet each and a height of the pyramid be 4 feet.

So, the base is a square with side length 5 feet.

And the height of the pyramid is 4 feet.

The volume of a pyramid is given by the formula:

$V=\frac{a^2 h}{3}$

Where

a is the square base side length (given as 5)

h is the height of the pyramid (given as 4)

Now we substitute and find the value:

$V=\frac{a^2 h}{3}\\V=\frac{(5)^2 (4)}{3}\\V=33.33$

The volume is around 33.33 cubic feet

5 0

2 years ago

The equation 2x2 − 12x + 1 = 0 is being rewritten in vertex form. Fill in the missing step. Given 2x2 − 12x + 1 = 0 Step 1 2(x2

Bezzdna [24]

Answer:

Part 1) $2(x-3)^{2}-17=0$ (the missing steps in the explanation)

Part 3) (8, 4); The vertex represents the maximum profit

Part 4) x = 3.58, 0.42

Part 5) x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

Part 6) 2(x − 7)2 + 118; x = $7

Part 7) The maximum height of the puck is 4 feet. −(x − 4)^2 + 6

Part 8) (x + 3)^2 − 4

Part 9) 2(x − 1)^2 = 4

Part 10) 8(x − 4)^2 + 592

Step-by-step explanation:

Part 1) we have

$2x^{2} -12x+1=0$

Convert to vertex form

step 1

Factor the leading coefficient and complete the square

$2(x^{2} -6x)+1=0$

$2(x^{2} -6x+9)+1-18=0$

step 2

$2(x^{2} -6x+9)+1-18=0$

$2(x^{2} -6x+9)-17=0$

step 3

Rewrite as perfect squares

$2(x-3)^{2}-17=0$

Part 3) we have

$f(x)=-x^{2}+16x-60$

we know that

This is the equation of a vertical parabola open downward

The vertex is a maximum

Convert to vertex form

$f(x)+60=-x^{2}+16x$

Factor the leading coefficient

$f(x)+60=-(x^{2}-16x)$

Complete the squares

$f(x)+60-64=-(x^{2}-16x+64)$

$f(x)-4=-(x^{2}-16x+64)$

Rewrite as perfect squares

$f(x)-4=-(x-8)^{2}$

$f(x)=-(x-8)^{2}+4$

The vertex is the point (8,4)

The vertex represent the maximum profit

Part 4) Solve for x

we have

$-2(x-2)^{2}+5=0$

$-2(x-2)^{2}=-5$

$(x-2)^{2}=2.5$

square root both sides

$(x-2)=(+/-)1.58$

$x=2(+/-)1.58$

$x=2(+)1.58=3.58$

$x=2(-)1.58=0.42$

Part 5) we have

$f(x)=-x^{2}+50x-264$

we know that

The zeros or x-intercepts are the value of x when the value of the function is equal to zero

In this context the zeros represent the number of monthly memberships where no profit is made

To find the zeros equate the function to zero

$-x^{2}+50x-264=0$

$-x^{2}+50x=264$

Factor -1 of the leading coefficient

$-(x^{2}-50x)=264$

Complete the squares

$-(x^{2}-50x+625)=264-625$

$-(x^{2}-50x+625)=-361$

$(x^{2}-50x+625)=361$

Rewrite as perfect squares

$(x-25)^{2}=361$

square root both sides

$(x-25)=(+/-)19$

$x=25(+/-)19$

$x=25(+)19=44$

$x=25(-)19=6$

Part 6) we have

$-2x^{2}+28x+20$

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

Factor the leading coefficient

$-2(x^{2}-14x)+20$

Complete the square

$-2(x^{2}-14x+49)+20+98$

$-2(x^{2}-14x+49)+118$

Rewrite as perfect square

$-2(x-7)^{2}+118$

The vertex is the point (7,118)

therefore

The video game price that produces the highest weekly profit is x=$7

Part 7) we have

$f(x)=-x^{2}+8x-10$

Convert to vertex form

$f(x)+10=-x^{2}+8x$

Factor -1 the leading coefficient

$f(x)+10=-(x^{2}-8x)$

Complete the square

$f(x)+10-16=-(x^{2}-8x+16)$

$f(x)-6=-(x^{2}-8x+16)$

Rewrite as perfect square

$f(x)-6=-(x-4)^{2}$

$f(x)=-(x-4)^{2}+6$

The vertex is the point (4,6)

therefore

The maximum height of the puck is 4 feet.

Part 8) we have

$x^{2}+6x+5$

Convert to vertex form

Group terms

$(x^{2}+6x)+5$

Complete the square

$(x^{2}+6x+9)+5-9$

$(x^{2}+6x+9)-4$

Rewrite as perfect squares

$(x+3)^{2}-4$

Part 9) we have

$2x^{2}-4x-2=0$

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 2 the leading coefficient

$2(x^{2}-2x)-2=0$

Complete the square

$2(x^{2}-2x+1)-2-2=0$

$2(x^{2}-2x+1)-4=0$

Rewrite as perfect squares

$2(x-1)^{2}-4=0$

$2(x-1)^{2}=4$

The vertex is the point (1,-4)

Part 10) we have

$8x^{2}-64x+720$

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert to vertex form

Factor 8 the leading coefficient

$8(x^{2}-8x)+720$

Complete the square

$8(x^{2}-8x+16)+720-128$

$8(x^{2}-8x+16)+592$

Rewrite as perfect squares

$8(x-4)^{2}+592$

the vertex is the point (4,592)

The population has a minimum at x=4 years ( that is after 4 years since 1998 )

6 0

2 years ago

You thought the balance in your checking account was $68 when you check your online account you realize that you forgot to recor

erma4kov [3.2K]

68-26 = 42 dollar check

3 0

3 years ago

Read 2 more answers

Which linear equation has no solution?

olga_2 [115]

Answer:

Option A

Step-by-step explanation:

Given:

a. 3x-5= 3x + 5
b. 3x-5= 3x - 5
c. 3x - 5 = 2x+5
d. 3x-5 = 2x + 10

To find:

Which one of the linear equations have no solution.

Solution:

a) 3x-5= 3x + 5

Add 5 to both sides

3x-5= 3x + 5

3x - 5 + 5 = 3x + 5 + 5

Simplify

(Add the numbers)

3x - 5 + 5 = 3x + 5 + 5

3x = 3x + 5 + 5

(Add the numbers)

3x = 3x + 5 + 5

3x = 3x + 10

Subtract 3x from both sides

3x = 3x + 10

3x - 3x = 3x + 10 - 3

Simplify

(Combine like terms)

3x -3x = 3x + 10 - 3

0 = 3x + 10 - 3

(Combine like terms)

0 = 3x + 10 - 3

0 = 10

The input is a contradiction: it has no solutions

b) 3x-5= 3x - 5

Since both sides equal, there are infinitely many solutions.

c) 3x - 5 = 2x+5

Add 5 to both sides

3x = 2x + 5 + 5

Simplify 2x + 5 + 5 to 2x + 10

3x = 2x + 10

Subtract 2x from both sides

3x - 2x = 10

Simplify 3x - 2x to x.

x = 10

d) 3x-5 = 2x + 10

Add 5 to both sides

3x = 2x + 10 + 5

Simplify 2x + 10 + 5 to 2x + 15

3x = 2x + 15

Subtract 2x from both sides

3x - 2x = 15

Simplify 3x -2x to x.

x = 15

--------------------------------------------

Answer:

As you can see all c and d both have solutions, eliminating them as options. Option B has infinite solutions leaving Option A which has no solutions.

Therefore, Option A is the linear equation that has no solution.

3 0

1 year ago

Read 2 more answers

Which of the following segments is a radius of OK? ОА. АМТ ОВ. Вт Ос. AMR O D. KM

FrozenT [24]

Answer:

A) TA

Step-by-step explanation:

A radius goes from the center of a circle to the outside edge.

RP connects two points on the outside edge of the circle without going through the center. This is not a radius.

TR connects two opposite points on the outside edge of the circle while going through the center. This is a diameter, not a radius.

GP connects two opposite points on the outside edge of the circle while going through the center. This is a diameter, not a radius.

TA connects the center of the circle to the outside edge. This is a radius.

8 0

2 years ago