Which expression is equivalent to
2/3(9x-6)+4(1/2 x -- 1/2)


1/2 and 3/4 are fractions

Answer:

Part 1) The perimeter of rectangle is equal to 24 units

Part 2) The area of rectangle is equal to 32 square units

Step-by-step explanation:

Part 1) Find the perimeter of rectangle

we know that

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

where

L is the length of rectangle

W is the width of rectangle

we have

[tex]F(-2,5),R(-2,1),O(6,1),G(6,5)[/tex]

Plot the figure to better understand the problem

using a graphing tool

see the attached figure

Remember that in a rectangle opposite sides are congruent and the measure of each interior angle is equal to 90 degrees

so

[tex]FG=RO=L\\RF=OG=W[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

step 1

Find the distance FG

[tex]F(-2,5),G(6,5)[/tex]

substitute the values

[tex]d=\sqrt{(5-5)^{2}+(6+2)^{2}}[/tex]

[tex]d=\sqrt{(0)^{2}+(8)^{2}}[/tex]

[tex]FG=8\ units[/tex]

step 2

Find the distance RF

[tex]R(-2,1),F(-2,5)[/tex]

substitute the values

[tex]d=\sqrt{(5-1)^{2}+(-2+2)^{2}}[/tex]

[tex]d=\sqrt{(4)^{2}+(0)^{2}}[/tex]

[tex]RF=4\ units[/tex]

step 3

Find the perimeter

[tex]P=2(L+W)[/tex]

we have

[tex]FG=RO=L=8\ units\\RF=OG=W=4\ units[/tex]

substitute

[tex]P=2(8+4)=24\ units[/tex]

Part 2) Find the area of rectangle FROG

we know that

The area of rectangle is equal to

[tex]A=LW[/tex]

we have

[tex]FG=RO=L=8\ units\\RF=OG=W=4\ units[/tex]

substitute

[tex]A=(8)(4)=32\ units^2[/tex]

The area and the perimeter of the rectangle FROG is evaluated as:

For a rectangle with length and width L and W units, we get:

The shortest distance(straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

[tex]D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]

The coordinates of the points of the rectangle FROG are given as:

F(-2,5), R(-2,1), G(6,5), and O(6,1) (from its plot, as given below)

FR and RO are length and width pair(we can call any one of them as length and other as width) of the considered rectangle as they are adjacent to each other.

We denote length of a line segment AB by |AB|

Thus, we get:

Now with the help of length and width, we can evaluate its perimeter and area, as shown below:

Learn more about distance between two points here:

https://brainly.com/question/16410393

Answer:

22. 150 minutes

23. ½ day

24. 0,045 minutes

25. 1,5 weeks

26. 1 year

The equation [tex]r=\sqrt\frac{V}{3.14h}[/tex] can be used to find the radius.

Step-by-step explanation:

Given,

Volume of large can;

V=πr(r)h

V=πr²h

Dividing both sides by πh

[tex]\frac{V}{\pi h}=\frac{r^2\pi h}{\pi h}\\\\\frac{V}{\pi h}=r^2\\\\r^2=\frac{V}{\pi h}[/tex]

Taking square root on both sides

[tex]\sqrt{r^2}=\sqrt{\frac{V}{\pi h}}\\r=\sqrt\frac{V}{\pi h}[/tex]

Putting π=3.14

[tex]r=\sqrt\frac{V}{3.14h}[/tex]

The equation [tex]r=\sqrt\frac{V}{3.14h}[/tex] can be used to find the radius.

Keywords: volume, square root

Learn more about square root at:

#LearnwithBrainly

The median of given data is 42.5

And

The median after replacing 42 with 92 is 44.5

Step-by-step explanation:

A median is the middle value of the data that divided the data in two equal parts

Given data is:

46 43 39 48 52 40 42 98 20 38

First of all, the data has to arranged in ascending order

20, 38, 39, 40, 42, 43, 46, 48, 52, 98

As the number of values is even, n=10, the median will be the average of middle two numbers

20, 38, 39, 40, 42, 43, 46, 48, 52, 98

[tex]Median = \frac{42+43}{2}\\=\frac{85}{2}\\=42.5[/tex]

The median is 42.5

Now,

Replacing 42 with 92

20, 38, 39, 40, 92, 43, 46, 48, 52, 98

The data has to be re-arranged

So,

20, 38, 39, 40, 43, 46, 48, 52, 92, 98

As the number of values is same,

[tex]New\ median = \frac{43+46}{2}\\=\frac{89}{2}\\= 44.5[/tex]

Hence,

The median of given data is 42.5

And

The median after replacing 42 with 92 is 44.5

Keywords: Median, mode

Learn more about median at:

#LearnwithBrainly

Answer:

C

Step-by-step explanation:

Note the diameter of a circle is twice the radius, thus

diameter = 2 × 19 = 38 cm → C

Answer:

w=-1

Step-by-step explanation:

-15w-6w+7w=14

-21w+7w=14

-14w=14

w=14/-14

w=-1

Answer:

-15w -6w +7w=14

- 21w+7w =14

-14w =14

divide both sides by 14

-w = -1

w = 1

Step-by-step explanation:

Answer:

250 Cookies

Step-by-step explanation:

First calculate the cookies decorated per hour

100 ÷ 2 = 50 cookies per hour

Number of cookies in 5 hours = 50 × 5

= 250 Cookies

Answer:

250

Step-by-step explanation:

Divide 100 by 2 to get the hourly rate which would be 50. Then take the hourly rate and multiply it by the number of hours given, 5. 5 multiplied by 50 equals 250 cookies

Answer:

The height variable should be represented by the y-axis on a scatterplot.

Step-by-step explanation:

The explanatory variable and independent variable are similar terms. When a variable is not at all dependent on any factor then it is called an explanatory variable. So, it must be plotted along the independent axis i.e. x-axis.

On the other hand, a response variable is an alternate term of the dependent variable and in our case height is a corresponding dependent variable of explanatory variable age.

Therefore, the height variable should be represented by the y-axis on a scatterplot. (Answer)

Answer:Height

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

1. find a, b, and c

a = 1

b = -3

c = 1

2. plug values into formula

x = [3 ± sqrt(9-4•1•1)] / 2

3. simplify

x = [3 ± sqrt(5)] / 2

This is B.

Answer:

Option b) is correct

ie., [tex]x=\frac{3\pm \sqrt{5}}{2}[/tex]

Step-by-step explanation:

Given quadratic equation is [tex]x^{2}-3x+1=0[/tex]

To find the solutions of given equation:

Solution of quadratic equation [tex]ax^{2}+bx+c=0[/tex]

[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex] where a,b, are coefficients of [tex]x^{2}[/tex] and x respectively and c is constant.

From the given quadratic equation a=1, b=-3 and c=1

[tex]x=\frac{-(-3)\pm \sqrt{(-3)^{2}-4(1)(1)}}{2(1)}[/tex]

[tex]x=\frac{3\pm \sqrt{9-4}}{2}[/tex]

[tex]x=\frac{3\pm \sqrt{5}}{2}[/tex]

Therefore Option b) is correct

ie., [tex]x=\frac{3\pm \sqrt{5}}{2}[/tex]

Answer:

x = 10 and x = -10

Step-by-step explanation:

Given the function

[tex]f(x)=\dfrac{5x^2+3x+6}{x^2-100}[/tex]

This function is undefied when the denominator equals to 0. Find these values for x:

[tex]x^2-100=0\\ \\(x-10)(x+10)=0\\ \\x-10=0\ \ \text{or}\ \ x+10=0\\ \\x=10\ \ \text{or}\ \ x=-10[/tex]

This means that vertical lines x = 10 and x = -10 are vertical asymptotes (the graph of the function f(x) cannot meet these lines because this function is undefined at x = 10 and x = -10)

Answer:

16=53

Step-by-step explanation:

12.9 x 14 .9 + 6= 12

Answer:

Step-by-step explanation:

In order to obtain the total amount that Monica was charged you should follow some steps.

How much was the net price? You can obtain this value either by clearing the x:

X * 5% = $1.50

X = $1.50 / 5%

Or by using simple rule of three:

If 5% is $1.50

Then 100% is X

So you obtain = $30

Now you just need to sum The net prices and the taxes

Net + tax = Total Charge

$30 + $1.5 = $31.5

Answer:

.08 cents rounded

Step-by-step explanation:

1.50x.05%=.075

Step-by-step explanation:

First, distribute the -4 to the parenthesis:

24a-22=-4+24a

Add 22 to both sides:

24a-22+22=-4+22+24a

Simplify:

24a=18+24a

Subtract 24a from both sides:

24a-24a=18+24a-24a

Simplify:

0=18

hope this helps :)

Answer:

y = -2x - 6

The y-intercept will be (0,-6)

One point will be at (1,-8)

The line will go downward since it is a negative slope

Step-by-step explanation:

y−2=−2(x+4)

Distribute

y - 2 = -2x - 8

Move the constant to the other side

y - 2 = -2x - 8

  +2 =        +2

y = -2x - 6

f(x) = 7 is a even function

Solution:

Given that we have to find the even function

A function is even if and only if f(–x) = f(x)

Steps to follow:

Replace x with -x and compare the result to f(x). If f(-x) = f(x), the function is even.

If f(-x) = - f(x), the function is odd.

If f(-x) ≠ f(x) and f(-x) ≠ -f(x), the function is neither even nor odd.

[tex]f(x) = (x - 1)^2[/tex]

Substitute x = -x in above function

[tex]f(-x) = (-x - 1)^2[/tex]

Thus [tex]f(-x) \neq f(x)[/tex]

So this is not a even function

f(x) = 8x

Substitute x = -x in above function

f(-x) = 8(-x) = -8x

Thus [tex]f(-x) \neq f(x)[/tex]

So this is not a even function

[tex]f(x) = x^2 - x[/tex]

Substitute x = -x in above function

[tex]f(-x) = (-x)^2 - (-x) = x^2 + x[/tex]

Thus [tex]f(-x) \neq f(x)[/tex]

So this is not a even function

f(x) = 7

f(-x) = 7

Thus f(-x) = f(x)

Thus it is a even function

Answer:

A

Step-by-step explanation:

edg verified

Answer:

Part 1) Equation of a perpendicular line is [tex]y=\frac{2}{3}x+4[/tex]

Part 2) Equation of a parallel line is [tex]y=-\frac{3}{2}x+\frac{21}{2}[/tex]

Step-by-step explanation:

Part 1) Find the equation of the line that is perpendicular to the given line and passes through the point (3, 6).

we have

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

The slope of the given line is [tex]m=-\frac{3}{2}[/tex]

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

so

The slope of the perpendicular line to the given line is equal to

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

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

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

[tex]point\ (3,6)[/tex]

substitute

[tex]y-6=\frac{2}{3}(x-3)[/tex]

Convert to slope intercept form

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

Isolate the variable y

[tex]y-6=\frac{2}{3}x-2[/tex]

[tex]y=\frac{2}{3}x-2+6[/tex]

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

Part 2) Find the equation of the line that is parallel to the given line and passes through the point (3, 6).

we have

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

The slope of the given line is [tex]m=-\frac{3}{2}[/tex]

Remember that

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

so

The slope of the parallel line to the given line is equal to

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

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

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

[tex]point\ (3,6)[/tex]

substitute

[tex]y-6=-\frac{3}{2}(x-3)[/tex]

Convert to slope intercept form

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

Isolate the variable y

[tex]y-6=-\frac{3}{2}x+\frac{9}{2}[/tex]

[tex]y=-\frac{3}{2}x+\frac{9}{2}+6[/tex]

[tex]y=-\frac{3}{2}x+\frac{21}{2}[/tex]

Answer:

y=sqrt(1/2x-25/2), -sqrt(1/2x-25/2).

Step-by-step explanation:

y=2x^2+25

x=2y^2+25

2y^2=x-25

y^2=1/2x-25/2

y=sqrt(1/2x-25/2), -sqrt(1/2x-25/2)

Good evening ,

Answer:

Look at the photo below for the answer.

:)

Step-by-step explanation:

To compare fractions, they need to have the same denominator.  So you need to find the least common multiple (LCM) of 10, 3, and 4.

To find the LCM, first write the prime factorizations.

3 = 3

4 = 2²

10 = 2×5

The LCM is the product of each factor raised to its highest exponent.

LCM = 2²×3×5

LCM = 60

Now we rewrite each fraction with this new denominator.

9/10 = 54/60

2/3 = 40/60

2/4 = 30/60

Answer:

You need to convert the numbers into the same format.

Step-by-step explanation:

If you want to keep them in fraction form, you need to find the least common multiple. This means the smallest number that can be divided by all of the denominators. For this example, the number would be 60, because 60/10 is 6, 60/3 is 2, and 60/4 is 15. Now that we know this, you need to make every denominator 60. You do this by multiplying the numerator by whatever you needed to multiply the denominator by to get 60. For example, you need to multiply 10 by 6 to get sixty, so you would multiply 9 by 6 as well. You would repeat this pattern with all of the numbers, getting 54/60 (9/10), 40/60 (2/3), and 30/60 (2/4). This makes it very easy to tell which is the larger number.

If you don't want to do all of that, you can use decimal form. To find what each number would be in decimal form, divide the numerator by the denominator. For example, 9 divided by ten is .9, 2 divided by 3 is .66..., and 2/4 is .5.

Answer:

D

Step-by-step explanation:

Find (f + g)(x) then evaluate (f + g)(9)

(f + g)(x) = f(x) + g(x)

= 4x - 1 + x² - 2 = x² + 4x - 3

Now substitute x = 9 into the expression

(f + g)(9) = 9² + 4(9) - 3 = 81 + 36 - 3 = 114 → D

Answer:

J.117

Step-by-step explanation:

f(x) =4x-1

if f(2)= 4(2)-1

f(2)= 8-1 = 7

f(2) = 7 equation 1

g(x) =x2-2

if g(4)= (4)2-2

g(4) = 8-2 = 6 equation 2

Now,

(f+g)(9) =?

subtitute equation 1 and 2

(7+6)(9)=?

(13)(9)=?

13×9= 117

Hence, the answer is 117

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

10,000,000

It is is the tens millions place.

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

｡☆✼★ ━━━━━━━━━━━━━━  ☾

Answer:

The eight place from the right.

Step-by-step explanation:

1, 10, 100, 1.000, 10.000, 100.000, 1.000.000, 10.000.000

Answer:

  -x^4y^2 +7x^3y^3 +2x^2y^4 -3xy^5

Step-by-step explanation:

The powers of x in the terms of the given expression are ...

  4, 3, 1, 2

so, we want to swap the last two terms to put them in the desired order:

  -x^4y^2 +7x^3y^3 +2x^2y^4 -3xy^5

Answer:

  x < -4 ∪ x > 4

Step-by-step explanation:

The absolute value function is shifted down 3 units. The solution space is values of x where y = |x|-3 is greater than 1. The solution is shown in red in the attachments, and the left and right (dashed) sides of the inequality are shown in blue.

__

I personally prefer to rewrite the inequality so the comparison is to zero. That is done in the second attachment, which rewrites it to ...

  |x| -4 > 0

by subtracting 1 from both sides. It is often easier to read the values of x-intercepts than it is to read the coordinate values where lines cross each other.

-18u+16u-7=9

-2u - 7 = 9       (combine like terms)

-2u = 16           (add 7 on both sides)

u = -8

Answer:

The correct answer to this problem is u = -8.

Step-by-step explanation:

To solve this problem, we first must combine like terms on the left side of the equation.  This means adding together the two terms that have a "u" multiplied by a number.  To combine them, we simply add the coefficients together, as we would with constant values.  This is modeled below:

-18u+16u-7=9

-2u - 7 = 9

Next, we want to add 7 to both sides of the equation.  This will cancel out the -7 on the left side of the equation, isolating the term with the variable u (what we are trying to solve for).

-2u - 7 + 7 = 9 + 7

-2u = 16

Finally, we want to divide both sides by -2 in order to isolate the variable u.  This will get rid of the coefficient of negative 2 and give us our answer.

u = 16/-2 = -8

Therefore, the answer to this question is u = -8.

Hope this helps!

Answer:

1. Vertical Angles Theorem

2. Converse of Alternate Interior Angles Theorem

Step-by-step explanation:

First option:

Lines AC and BD intersect at point E. Angles AEB and CED are opposite angles formed when these two lines intersect and are called vertical angles. By vertical angles theorem, these angles are congruent. So,

Vertical Angles Theorem

Second option:

[tex]\triangle BEC\cong \triangle DEA[/tex] by SAS postulate, then

[tex]\angle CBE\cong \angle ADE[/tex] as corresponding sides of congruent triangles.

Converse of Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

So, [tex]\overline{BC}\cong \overline{AD}[/tex] by

Converse of Alternate Interior Angles Theorem

Answer:

1.B            2.B

Step-by-step explanation:

Answer: [tex]\frac{1}{64}[/tex]

Step-by-step explanation:

We have the following equation:

[tex](2N)(5^{2})=\frac{25}{32}[/tex]

Isolating [tex]N[/tex]:

[tex](2N)(25)=\frac{25}{32}[/tex]

[tex]2N=\frac{25}{(32)(25)}[/tex]

[tex]N=\frac{1}{(32)(2)}[/tex]

Finally:

[tex]N=\frac{1}{64}=0.0156[/tex]

Answer:

B) f(x) ≥ 3x + 4

g of x is less than or equal to negative one half times x minus 5

Step-by-step explanation:

hope it helps

Answer:

The Answer is B.

f(x) ≥ 3x + 4

g(x) ≤ -1/2x - 5

Hope This Helps!

Answer:

4:24 p.m.

Step-by-step explanation:

Figure out how often the buses leave at the same time. This is the same as the least common multiple (LCM) of how often they leave the stadium.

The LCM is found by multiplying the maximum number of each prime factor found in any of the numbers.

The prime factors of a number are found by dividing it by whole numbers until the factors are all prime. Prime numbers only have the factors 1 and itself.

6 = 2 X 3

8 = 2 X 2 X 2

The greatest times 2 repeats is three times.

The greatest times 3 repeats is one time.

2 X 2 X 2 X 3 = 24

The LCM is 24, and the buses have the same leaving times every 24 minutes.

Find 24 minutes after 4:00 p.m. Change the minutes only, which are the numbers right of the colon : .

The buses will next leave together at 4:24 p.m.

Answer:

(1) 5 , PI + 2, 17/3

(2) 3/2, sqrt (5), 2.5

(3) Sqrt(5)/2, PI – 2, 5/4

Step-by-step explanation:

For each number, begin by comparing the whole numbers. The one with the least whole number is the smallest while the one with the largest is the biggest number.

If the numbers being compared have the same whole numbers, check the decimal places. Begin with tenths. The one with the lowest number is the smallest number. If they are the same compare the hundredths, if they are the same compare thousandths...until you find a decimal that is different and can differentiate the numbers.

Learn More:

https://brainly.com/question/11506796

https://brainly.com/question/11410123

#LearnWithBrainly

Answer:

its the letter w

Step-by-step explanation:

i got an 100 on the test