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2 months ago

Guest #9817

2 months ago

The side lengths of a square is equal, thus length=width, hence the dimensions of our square will be:

length=width=7 ft

hence;

area=length×width

area=7×7

area=49 ft²

Answer:

C.

49 ft2

length=width=7 ft

hence;

area=length×width

area=7×7

area=49 ft²

Answer:

C.

49 ft2

Question

Two mechanics worked on a car. the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800. what was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour ?

Solution 1

The **rates **charged per hour by the first and second **mechanics **will be $105 and $50.

It is defined as the relation between two **variables**, if we plot the graph of the **linear equation **we will get a **straight line**.

If in the linear equation, one **variable **is present, then the **equation **is known as the linear **equation **in one variable.

It is given that two mechanics worked on a car, the first **mechanic **worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800.

Suppose x is the **hourly rate **for the first mechanic and y is the hourly rate of the second.

If the total money earned is 1800.

10x + 15 y = 1800 ---- (1)

If both have their individual rates the sum of the **hourly rate **is,

x+ y = 15 -------- (2)

Rearrange the equation,

x = 155- y

Substitute the value of x in **equation **1 we get,

10x + 15 y = 1800

10(155-y) + 15y = 1800

1150 - 10y + 15y = 1800

5y = 250

y = 50

Substitute the value of y in **equation **2 we get,

x = 155- y

x= 155 - 50

x = 105

Thus, the **rates **charged per hour by the first and second **mechanics **will be $105 and $50.

Learn more about the **linear equation **here:

#SPJ2

Solution 2

This can be solved by setting up a systems of equations. Let x be the hourly rate for the first mechanic and y be the hourly rate of the second.

Total money earned:

Sum of hourly rates:

To solve this, you solve for one equation first, substitute it in the second, then input it back into the first equation. I will first be solving for x.

Input this into the other equation to find y:

Input y into the first equation:

The first mechanic charges $105 per hour and the second mechanic charges $50 per hour.

Total money earned:

Sum of hourly rates:

To solve this, you solve for one equation first, substitute it in the second, then input it back into the first equation. I will first be solving for x.

Input this into the other equation to find y:

Input y into the first equation:

The first mechanic charges $105 per hour and the second mechanic charges $50 per hour.

Question

Marie is buying an ice-cream sundae. There are 3 sizes of sundaes, 15 different ice-cream flavors, and 5 different toppings. How many ways can Marie choose a sundae?

Solution 1

Since each size of sundae has 15 flavor choices, we can find the number of combinations by multiplying the size of sundaes with the different ice cream flavors. The same rule can be applied to the number of different toppings, so you can set up this equation:

Multiplying them out, you can see that there are 225 different combinations of sundaes

Multiplying them out, you can see that there are 225 different combinations of sundaes

Solution 2

225 different ways, because 3 x 15 x 5 = 225.

Question

How many terms are in the arithmetic sequence 6, 2, −2, …, −102? Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference
27
28
29
30

Solution 1

The number of sequence in the arithmetic sequence given by:

6, 2, −2, …, −102

will evaluated as follows:

the explicit formula is:

an=a1+d(n-1)

a1=first term

d=common difference

n=number of terms

thus from the question:

a1=6

d=2-6=-4

an=-102

plugging the values in the expression we get:

-102=6-4(n-1)

solving for n we shall have:

-102-6=-4(n-1)

-108=-4(n-1)

27=n-1

thus

n=27+1

n=28

Answer: 28 terms

6, 2, −2, …, −102

will evaluated as follows:

the explicit formula is:

an=a1+d(n-1)

a1=first term

d=common difference

n=number of terms

thus from the question:

a1=6

d=2-6=-4

an=-102

plugging the values in the expression we get:

-102=6-4(n-1)

solving for n we shall have:

-102-6=-4(n-1)

-108=-4(n-1)

27=n-1

thus

n=27+1

n=28

Answer: 28 terms

Question

How to work out halfway between 1.1 and 1.2

Solution 1

Add the two numbers, then find one half of their sum.

Question

The line represented by y = 3x − 6 and a line perpendicular to it intersect at R(3, 3). What is the equation of the perpendicular line? A)y=-1/3x +4
B)y=1/3x + 7/3
C)y=-1/2x +5/2
D)y=-3x + 5

Solution 1

The answer is (A)

opposite slop

Flip the original slop and change the sign

The equation gonna be like (A)

y-intercept is doesn't matter same or different

hope it's help

opposite slop

Flip the original slop and change the sign

The equation gonna be like (A)

y-intercept is doesn't matter same or different

hope it's help

Question

Lin is 7 years younger than Adrian, Adrian is 4 years older than half of Maya's age,
The sum of the 3 ages is 61,
How old is Lin?

Solution 1

Answer: Age of Lin is 12

Solution:

Let X= age of Maya

(X/2)+4= age of Adrian

((X/2)+4)-7= age of Lin

X+(X/2)+4+((X/2)+4-7)=61

X+.5X+4+.5X+4-7=61

2X+4+4-7=61

2x=61-8+7

2X=60

X=30 age of Maya

19= age of Adrian

Age of Lin is

=((X/2)+4)-7

=15+4-7

=12

To check if this is correct

30+19+12=61

Question

How do you convert cos(x) into sin(x) and tan(x) ?

Solution 1

Since tan x = sin x / cos x, we could write:

tan x

cos x = ---------- In other words, rewrite "cos x" in an expression as

tan x

-----------

sin x

tan x

cos x = ---------- In other words, rewrite "cos x" in an expression as

tan x

-----------

sin x

Question

The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7. if in the last game he made 77 assists, how many standard deviations is that from the mean? 1.36 standard deviations below the mean 2.71 standard deviations above the mean 1.36 standard deviations above the mean 2.71 standard deviations below the mean

Solution 1

**Answer:**

(B)

**Step-by-step explanation:**

It is given that The number of assists per match for the setter on your school's volleyball team has a mean of 58 and a standard deviation of 7.

Also, in the last game he made 77 assists, therefore

assists away from the mean.

Thus, To get the number of standard deviation that 77 is from the mean, we get the z-score which is given as:

Substituting the given values, we get

**Thus, there are 2.71 standard deviations above the mean.**

**Hence, option B is correct.**

Solution 2

Given that mean=58

standard deviation=7

thus

77 is (77-58)=18 away from 58

This will be:

19/7=2.71

standard deviations from the mean.

Answer: 2.71 standard deviations above the mean

standard deviation=7

thus

77 is (77-58)=18 away from 58

This will be:

19/7=2.71

standard deviations from the mean.

Answer: 2.71 standard deviations above the mean

Question

Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers shee can drive with 12 liters of fuel. How many kilometers can Pamela drive with 12 liters of fuel?

Solution 1

**Answer:**

132 km

**Step-by-step explanation:**

1. she can drive 99 km (kilometers) with 9 liters of fuel, 99/9 is 11

2. if she wants to find out how many kilometers she can drive with 12 liters of fuel, then just multiply 12x11 which is 132

Solution 2

121 kilometers. The ratio of kilometers to liters of gas is 11:1. Then you substitute the 1 for twelve and multiply 11 by 12. The answer is 121 kilometers.

Question

Simplify. x-2/(x^2+4x-12)

Solution 1

Simplifying the above expression we shall proceed as follows:

x-2/(x^2+4x-12)

factoring out the denominator we get:

x^2+4x-12

=x^2-2x+6x-12

=x(x-2)+6(x-2)

=(x+6)(x-2)

thus our expression will be:

(x-2)/[(x+6)(x-2)]

simplifying the above we get:

1/(x+6)

Answer: 1/(x+6)

x-2/(x^2+4x-12)

factoring out the denominator we get:

x^2+4x-12

=x^2-2x+6x-12

=x(x-2)+6(x-2)

=(x+6)(x-2)

thus our expression will be:

(x-2)/[(x+6)(x-2)]

simplifying the above we get:

1/(x+6)

Answer: 1/(x+6)

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