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3 years ago

12

Frick and frack are surveying the times it takes students to arrive at school from home. There are 2 main groups of commuters wh

o were in the survey.

1 answer:

noname [10]3 years ago

6 0

Answer:

900

Step-by-step explanation:

divide 4

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If zeba were younger by 5 years than what she really is then the square of her age would have been 11 more than five times her a

RSB [31]

Answer:

14 years old

Step-by-step explanation:

<u>Define the variable</u>

Let x be the actual age of Zeba (in years).

<u>Create an equation</u> using the give information and the variable x:

$(x - 5)^2=5x+11$

To find Zeba's age now, <u>solve the equation for x</u>.

Expand the brackets:

$\implies x^2-10x+25=5x+11$

Subtract 5x from both sides:

$\implies x^2-10x+25-5x=5x+11-5x$

$\implies x^2-15x+25=11$

Subtract 11 from both sides:

$\implies x^2-15x+25-11=11-11$

$\implies x^2-15x+14=0$

<u>Factor the found quadratic</u>

To factor a quadratic in the form $ax^2+bx+c$ <em>, </em>find two numbers that multiply to $ac$ and sum to $b$ , then rewrite $b$ as the sum of these two numbers:

$\implies x^2-14x-x+14=0$

Factor the first two terms and the last two terms separately:

$\implies x(x-14)-1(x-14)=0$

Factor out the common term (x - 14):

$\implies (x-1)(x-14)=0$

Apply the <u>zero product property</u>:

$\implies (x-1)=0 \implies x=1$

$\implies (x-14)=0 \implies x=14$

Therefore, Zeba's age now is either 1 or 14 years.

As the question states "If Zeba were younger by 5 years" then 1 must be an <u>extraneous solution</u> since 1 - 5 = -4 and Zeba cannot be -4 years old.

Therefore, Zeba's age now is 14 years old.

<u>Check</u>

Given the actual age of Zeba is 14 years old.

Therefore, If Zeba were younger by 5 years, she would be 9 years old as: 14 - 5 = 9

The square of 9 is: 9² = 81.

5 times her actual age: 5 × 14 = 70

81 is 11 more than 70, hence verifying that her <u>actual age is 14 years old</u>.

Learn more about quadratic equations here:

brainly.com/question/27956741

brainly.com/question/27947331

5 0

1 year ago

Read 2 more answers

Choose 2 hellllpppppp plzzzxxxxzz

diamong [38]

Answer:

Choices C and D

Step-by-step explanation:

The most simplest way is just to solve each one and see which two have the same answer as the first expression.

But you could also see that both of the $\frac{4}{7}$ are going to cancel each other out so you are left with $-\frac{8}{9} +\frac{9}{8}$ which is also choice C.

For choice D I distributed the negative one to the insides of the parenthesis that left me with $-\frac{4}{7}-\frac{8}{9}+\frac{4}{7} +\frac{9}{8}$ which is the same expression as the first one.

5 0

2 years ago

For the region bounded by y=2x, the x-axis, and x=1, determine which of the following is greater: the volume of the solid ge

telo118 [61]

Answer:

The correct answer B) The volumes are equal.

Step-by-step explanation:

The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,

$\int\limits^1_0 {(pi)y^{2} } \, dx$

which when evaluated gives 4pi/3.

Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,

$\int\limits^2_0 {pi - pix^{2} } \, dy = \int\limits^2_0 {1 - y^{2}/4 } \, dy$

If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.

7 0

3 years ago

Joanna has 70 beads. She uses 8 beads for each bracelet. She makes as many bracelets as possible. How many beads will Joanna hav

gogolik [260]

She will have 6 braces left over since 8x8=64 and 70-64=6

6 0

3 years ago

Read 2 more answers

How do you us the distributive property to work out (4+5)6

777dan777 [17]

During Distributive property, the number on the outside of the parenthesis basically gets multiplied by the numbers inside the parenthesis. In this case, you would multiply 6 by 5 and 4. When you get the products, then follow the sign that comes next. In this case, you would add the products to get a total sum. I attached a photo for further reference.
Hope this helps!

7 0

3 years ago

Read 2 more answers