16: Simplify V x W x X

Answer: Usually, a denominator should be bigger. If the numerator was bigger, it would make the fraction inproper, which you should convert into a mixed number.

Answer:denominator

Step-by-step explanation:

Answer:

x^2/3

Step-by-step explanation:

(x^5/6)/(x^1/6)=x^(5/6-1/6)=x^4/6

simplify 4/6, you get 2/3.

Answer:a total of 45 students per bus

Step-by-step explanation: 450-5= 445

445/10= 44.5

a total of 45 students per bus

Answer:

Part 40) [tex]y=-2x+9[/tex]

Part 41) [tex]y=5x+6[/tex]

Part 42) [tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]

Step-by-step explanation:

Remember that

If two lines are parallel, then their slopes are the same

Part 40) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (4,1)

Given line y=-2x+7

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

so

The slope of the given line is

[tex]m=-2[/tex]

step 2

Find the y-intercept b

we have

[tex]m=-2[/tex]

[tex](4,1)[/tex]

substitute in the linear equation

[tex]1=(-2)4+b[/tex]

solve for b

[tex]b=1+8[/tex]

[tex]b=9[/tex]

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

[tex]m=-2[/tex]

[tex]b=9[/tex]

substitute

The equation of the line is

[tex]y=-2x+9[/tex]

Part 41) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (0,6)

Given line y=5x-3

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

so

The slope of the given line is

[tex]m=5[/tex]

step 2

Find the y-intercept b

[tex]b=6[/tex] ----> because the y-intercept is the point (0,6) (value of y when the value of x is equal to zero)

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

[tex]m=5[/tex]

[tex]b=6[/tex]

substitute in the linear equation

[tex]y=5x+6[/tex]

Part 42) Write an equation of the line that passes through the given point

and is parallel to the given line

we have

Point (-5,-2)

Given line y=(2/3)x+1

step 1

Find the slope of the given line

The given line is a equation of the line in slope intercept form

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

so

The slope of the given line is

[tex]m=\frac{2}{3}[/tex]

step 2

Find the y-intercept b

we have

[tex]m=\frac{2}{3}[/tex]

[tex](-5,-2)[/tex]

substitute in the linear equation

[tex]-2=(\frac{2}{3})(-5)+b[/tex]

solve for b

[tex]-2=-\frac{10}{3}+b[/tex]

[tex]b=-2+\frac{10}{3}[/tex]

[tex]b=\frac{4}{3}[/tex]

step 3

Find equation of the line that passes through the given point and is parallel to the given line

we have

[tex]m=\frac{2}{3}[/tex]

[tex]b=\frac{4}{3}[/tex]

substitute

The equation of the line is

[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]

Final answer:

To find the equation of a line that is parallel to a given line and passes through a specific point, use the fact that parallel lines have the same slope. Find the slope of the given line, substitute the slope and the point into the slope-intercept form of a line to find the y-intercept, and write the equation with the new slope and y-intercept.

Explanation:

To find the equation of a line that is parallel to a given line and passes through a specific point, we need to use the fact that parallel lines have the same slope. The given line, y = -2x + 7, has a slope of -2. So, the parallel line we need to find will also have a slope of -2.

Now, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. Since we know the slope is -2 and the point (4,1) lies on the line, we can substitute these values into the equation to find the y-intercept:

y = -2x + b

1 = -2(4) + b

1 = -8 + b

b = 9

Therefore, the equation of the line that passes through (4,1) and is parallel to y = -2x + 7 is y = -2x + 9.

Answer:

Twice.

Step-by-step explanation:

7 times 2 is 14.

So it can only go in 2x.

Answer:

Seven goes into 18 twice

Step-by-step explanation:

7×2=14

Answer:

He can spend $1363 for everything else.

Step-by-step explanation:

x+637<=2000

x<=2000-637

x<=1363

Answer:9 nickels and 19 dimes.

Step-by-step explanation:

Let [tex]n[/tex] be the number of nickels Kay has.

Let [tex]d[/tex] be the number of dimes Kay has.

Value of [tex]1[/tex] nickel is $[tex]0.05[/tex]

Value of [tex]n[/tex] nickels is $[tex]0.05n[/tex]

Value of [tex]1[/tex] dime is $[tex]0.1[/tex]

Value of [tex]d[/tex] nickels is $[tex]0.1dn[/tex]

Given that Kay has a total of [tex]28[/tex] coins.

So,[tex]n+d=28[/tex]                                                ...(i)

Given that Kay has a total value of $[tex]2.35[/tex]

So,[tex]0.05n+0.1d=2.35[/tex]                                 ...(ii)

Using (i) and (ii),

[tex]0.05n+0.1(28-n)=2.35\\0.05n+2.8-0.1n=2.35\\2.8-2.35=0.05n\\0.45=0.05n\\n=9[/tex]

[tex]d=28-n=28-9=19[/tex]

Answer: slope m = (y2 - y1)/(x2 - x1) so that  m = (2-(-1))/(5.3-4.5)

m = 3 / .8 = 3.75 or 15/4

Step-by-step explanation:

Answer:

Lin needs 12.53 square feet of fabric

Step-by-step explanation:

we know that

The area of the window covering is equal to the area of the square plus the area of semicircle

step 1

Find the area of the square

The area of the square is equal to

[tex]A_1=b^{2}[/tex]

where

b is the length side of the square

we have

[tex]b=3\ ft[/tex]

substitute

[tex]A_1=3^{2}=9\ ft^2[/tex]

step 2

Find the area of semicircle

The area of semicircle is equal to

[tex]A_2=\frac{1}{2}\pi r^{2}[/tex]

The length side of the square is equal to the diameter of semicircle

so

[tex]r=3/2=1.5\ ft[/tex] ----> the radius is half the diameter

assume

[tex]\pi =3.14[/tex]

substitute

[tex]A_2=\frac{1}{2}(3.14)(1.5)^{2}[/tex]

[tex]A_2=3.53\ ft^2[/tex]

Adds the areas

[tex]A=A_1+A_2[/tex]

[tex]A=9+3.53=12.53\ ft^2[/tex]

therefore

Lin needs 12.53 square feet of fabric

Final answer:

Lin needs approximately 12.54 square feet of fabric for a window covering with a half-circle on top of a square, both with a side length of 3 feet. Calculating the areas of the square and the half-circle and summing them gives the total fabric required.

Explanation:

To calculate the amount of fabric Lin needs for the window covering with a half-circle on top of a square with a side length of 3 feet, we need to find the area of both the square and the half-circle and add them together. The area of the square is straightforward - since all sides are equal, the area is side × side, which is 3 feet × 3 feet = 9 square feet. For the half-circle, we first need to calculate the area of a full circle using the formula πr² (where π is pi, approximately 3.14159, and r is the radius of the circle). The diameter of the circle is the same as the side length of the square, which is 3 feet, making the radius 1.5 feet.

So, the area of a full circle is π × (1.5 feet)² = π × (2.25 square feet).

To find the area of the half-circle, we simply divide this by 2, resulting in π × 2.25 square feet / 2 = 3.53429174 square feet. Adding the area of the square and the half-circle gives us the total fabric needed: 9 square feet + 3.53429174 square feet = 12.53429174 square feet.

Therefore, Lin needs approximately 12.54 square feet of fabric for her window covering.

Answer:

[tex]\frac{x}{-3} =6\\x=-18[/tex]

x= -18

Answer: X = -18

Step-by-step explanation: In this problem, notice that x is being divided by -3 so to get x by itself, we need to multiply both sides of the equation by -3.

Notice that on the left side, the -3 and -3 cancel each other out so we're just left with x.

On the right side, we have 6 × -3 which is -18 so X = -18.

Finally, we can check our answer by plugging a -18 back into the original equation.

So we have -18 ÷ -3 = 6, which is a true statement which means that our answer is correct.

Image provided.

Answer:

The final price is $ 22.68  And Proportional constant is 1.4  

Step-by-step explanation:

Given as :

The Original price = $ 16.20

The rate of increase = 40%

Let The final price = x

Now,

Final price after increase = initial price × ( 1 + [tex]\frac{\textrm Rate}{100}[/tex]

Or. Final price after increase = $ 16.20 × ( 1 + [tex]\frac{\textrm 40}{100}[/tex]

Or, Final price after increase = $ 16.20 × ( 1.4 )

∴ Final price after increase = $ 22.68

Now , Proportional constant = [tex]\frac{22.68}{16.20}[/tex]

I.e Proportional constant = 1.4

Hence The final price is $ 22.68  And Proportional constant is 1.4  Answer

Answer:

⇒[tex](Base)^2 + ( Perpendicular)^2 = (Hypotenuse)^2[/tex]  is the required relationship.

Step-by-step explanation:

Let us assume, the given right angled triangle is ΔPQR.

Here. PQ = Perpendicular of the triangle.

QR = Base of the triangle.

PR = Hypotenuse of the triangle.

Now, PYTHAGORAS THEOREM states:

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“

⇒[tex](Base)^2 + ( Perpendicular)^2 = (Hypotenuse)^2[/tex]

Hence in ΔPQR:  [tex](QR)^2 + ( PQ)^2 = (PR)^2[/tex]

And the above expression is the required relationship between the sides of a right triangle.

The sides of a right triangle have a specific relationship given by the Pythagorean Theorem, which states a² + b² = c², where a and b refer to the lengths of the sides and c refers to the length of the hypotenuse. Additionally, the sides have relationships to the angles of the triangle expressed through trigonometric functions.

The relationship between the sides of a right triangle is given by the Pythagorean Theorem which was demonstrated by the ancient Greek philosopher, Pythagoras. This theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, if the lengths of the sides are a, b, and c (where c represents the length of the hypotenuse), then the relationship can be represented as a² + b² = c².

Moreover, the sides of a right triangle also have specific relationships to the measures of the angles of the triangle, which are expressed through the trigonometric functions sine, cosine, and tangent. For example, for an angle in a right triangle, the sine is the length of the opposite side divided by the length of the hypotenuse, the cosine is the length of the adjacent side divided by the hypotenuse, and the tangent is the length of the opposite side divided by the adjacent side.

https://brainly.com/question/28361847

#SPJ12

Answer:

[tex]17 + \frac{ - 18}{6} = 17 - 3 = 14[/tex]

Answer:

27 cats.

Step-by-step explanation:

The fraction of cats = 9 / (9 + 13) and dogs = 13 / ( 9 + 130

= 9/22 and 13/22

So the number of cats = (9/22) * 66

= 9 *3

= 27.

=

Answer:

$12159 per year.

Step-by-step explanation:

If I invest $x each year at the simple interest of 7.5%, then the first $x will grow for 35 years, the second $x will grow for 34 years and so on.

So, the total amount that will grow after 35 years by investing $x at the start of each year at the rate of 7.5% simple interest will be given by

[tex]x( 1 + \frac{35 \times 7.5}{100}) + x( 1 + \frac{34 \times 7.5}{100}) + x( 1 + \frac{33 \times 7.5}{100}) + ......... + x( 1 + \frac{1 \times 7.5}{100})[/tex]

= [tex]35x + \frac{x \times 7.5}{100} [35 + 34 + 33 + ......... + 1][/tex]

= [tex]35x + \frac{x \times 7.5}{100} [\frac{1}{2} (35) (35 + 1)][/tex]

{Since sum of n natural numbers is given by [tex]\frac{1}{2} (n)(n + 1)[/tex]}

= 35x + 47.25x

= 82.25x

Now, given that the final amount will be i million dollars = $1000000

So, 82.25x = 1000000

⇒ x = $12,158. 05 ≈ $12159

Therefore. I have to invest $12159 per year. (Answer)

Answer: losing weight from 50lb to 40lb

Step-by-step explanation:

Answer:

50lb to 40lb

Step-by-step explanation:

When you multiply 50 lb to 40lb by 2, it makes 100 lb to 80 lb. 50lb to 40 lb is 20 percent change while 100 lb to 90 lb is 10 percent

Answer:

x=-1, y=-5. (-1, -5).

Step-by-step explanation:

y=-x-6

y=x-4

----------

-x-6=x-4

-x-x-6=-4

-2x-6=-4

-2x=-4+6

-2x=2

x=2/-2

x=-1

y=-1-4

y=-5

Answer:

Step-by-step explanation:

Hajdiabndodisba djdk

Answer:

4.924 units.

Step-by-step explanation:

See the attached diagram.

If P is the midpoint of AB and Q is the midpoint of AC, then PQ is parallel to BC and the length of PQ will be half of BC.

Now, the coordinates of B are (1,1) and that of C is (10,-3).

Therefore the length of BC is [tex]\sqrt{(10 - 1)^{2} + (- 3 - 1)^{2}} = 9.848[/tex] units (Approximate)

Therefore, the length of PQ = 0.5 × 9.848 = 4.924 units. (Answer)

We know that the distance between two given points ([tex]x_{1},y_{1}[/tex]), and ([tex]x_{2},y_{2}[/tex]) is given by the formula

[tex]\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}[/tex]

He sold 32 small watermelons and 17 large watermelons.

Step-by-step explanation:

Let,

Small watermelons = x

Large watermelons = y

Cost of one small watermelon = $7

Cost of one large watermelon = $10

According to given statement;

x = y+15   Eqn 1

7x+10y=394   Eqn 2

Putting value of x from Eqn 1 in Eqn 2

[tex]7(y+15)+10y=394\\7y+105+10y=394\\17y=394-105\\17y=289\\[/tex]

Dividing both sides by 17

[tex]\frac{17y}{17}=\frac{289}{17}\\y=17[/tex]

Putting y=17 in Eqn 1

[tex]x=17+15\\x=32[/tex]

He sold 32 small watermelons and 17 large watermelons.

Keywords: linear equations, substitution method

Learn more about linear equations at:

#LearnwithBrainly

Answer:

Step-by-step explanation:

Answer:

Total bill=$51.75

Step-by-step explanation:

Step 1: Determine the cost of her meal

Cost of meal=$45

Step 2: Calculate the amount of the tip

Tip amount=15% of the cost of meal

where;

cost of meal=$45

replacing;

Tip amount=(15/100)×45=6.75

The tip amount=$6.75

Step 3: Total bill

The total bill can be expressed as;

Total bill=tip amount+subtotal

where;

tip amount=$6.75

cost of meal=$45

replacing;

Total bill=(45+6.75)=51.75

Total bill=$51.75

Answer:

x=8

Step-by-step explanation:

You divide both sides by 4 to get x alone.

Answer:

x = 8

Step-by-step explanation:

Answer: The answer is 32

Answer:

32

Step-by-step explanation:

25%=0.25

8/0.25=32

To convert 2 meters to inches, you multiply by the conversion factor of approximately 39.37, resulting in 78.7 inches when rounded to the nearest tenth.

The measurement 2 meters is equivalent to

78.7 inches.

To convert meters to inches, we know that 1 meter is approximately 39.37 inches. Therefore, 2 meters would be equal to 2 x 39.37 = 78.74 inches. Rounding to the nearest tenth, this equals 78.7 inches.

The mean score on this test is 8.8, and the median score is 9.4.

In order to find the mean of the scores, we use the formula:

[tex]\[ \text{Mean} = \frac{\sum (X \cdot f)}{N} \][/tex]

where X is the score, f is the frequency, and N is the total number of scores. Applying this formula to the given data:

[tex]\[ \text{Mean} = \frac{(4 \cdot 1) + (5 \cdot 1) + (6 \cdot 1) + (7 \cdot 2) + (8 \cdot 1) + (9 \cdot 5) + (10 \cdot 5)}{1 + 1 + 1 + 2 + 1 + 5 + 5} \][/tex]

[tex]\[ \text{Mean} = \frac{4 + 5 + 6 + 14 + 8 + 45 + 50}{15} \][/tex]

Mean = [tex]\frac{132}{15}[/tex]

Mean = 8.8

So, the mean score is 8.8.

To find the median using the formula:

[tex]\[ \text{Median} = L + \frac{\frac{N}{2} - F}{f} \times w \][/tex]

where:

- L is the lower class boundary of the median group,

- N is the total number of observations,

- F is the cumulative frequency of the group before the median group,

- f is the frequency of the median group,

- w is the width of the median group.

First, arrange the data and calculate cumulative frequencies:

Test Score  Frequency     Cumulative Frequency

3                    0                      0

4                      1                      1

5                      1                     2

6                       1                     3

7                       2                     5

8                       1                      6

9                       5                     11

10                     5                     16

The median position is [tex]\( \frac{N}{2} = \frac{16}{2} = 8 \)[/tex]  with a score of 9. The cumulative frequency before the median group is 6, and the frequency of the median group is 5.

Now, using the formula:

Median= 9 + [tex]\frac{8 - 6}{5} \times 1[/tex]

Median= 9 + [tex]\frac{2}{5}[/tex]

Median = 9 + 0.4

Median = 9.4

Therefore, the median score is 9.4.

Answer:

40

Step-by-step explanation:

8 / (1/5)

When dividing fractions, the second fraction just flips upside down. Then you just multiply.

So it's now 8 * 5 = 40

Answer:

300.407

Step-by-step explanation:

100*3=300

4*0.1=0.4

7*0.001=0.007

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

300+0.4+0.007

300.407

Answer:

False

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

[tex]A=10^0[/tex]

Step-by-step explanation:

Number 2.247 has 2 in ones place, 2 in tenths place, 4 in hundredths place and 7 in thousandths place.

This means you can rewrite this number as

[tex]2.247=2\times 1+2\times 0.1+4\times 0.01+7\times 0.001\\ \\2.247=2\times 10^0+2\times \dfrac{1}{10^1}+4\times \dfrac{1}{10^2}+7\times \dfrac{1}{10^3}[/tex]

So,

[tex]A=10^0\\ \\B=\dfrac{1}{10^1}\\ \\C=\dfrac{1}{10^2}\\ \\D=\dfrac{1}{10^3}[/tex]