combine like terms to simplify the expression. 2x+4y-7x+10y+8

Answer: The coordinates of the midpoint of diagonal AC are [tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]. The coordinates of the midpoint of diagonal BD are  [tex](\frac{a+b}{2} , \frac{c}{2} )[/tex] AC and BD  intersect at point E with coordinates [tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]. By the definition of midpoint, CE ≅ EA and BE ≅ ED Therefore, diagonals AC and BD bisect each other.

Step-by-step explanation:

Since, here the coordinates of A ≡ (0,0) B ≡ (a, 0) D≡ ( b,c)

And, here ABCD is the parallelogram.

Therefore AB = CD

If y is the y-coordinate of C Then C≡(a+b, y)

⇒ [tex]a^2 + 0 = (a)^2 + (y-c)^2[/tex]

⇒ y =c

Thus, C≡(a+b, c)

The coordinates of the midpoint of diagonal AC are,

[tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]

And,  The coordinates of the midpoint of diagonal BD are,

[tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]

Since, by the below diagram AC and BD are intersecting at point E,

Where the  coordinates of E are,

[tex](\frac{a+b}{2} , \frac{c}{2} )[/tex]

Thus, E is the mid point of Both the segments AC and BD

Because, BE = ED and AE = EC

Therefore, we can say that both AC and BD bisect each other.

Answer:

the coordinate point C are (a+b,c)

The coordinates of the midpoint of diagonal AC¯¯¯¯¯ are (a+b/2, c/2)

The coordinates of the midpoint of diagonal BD¯¯¯¯¯ are (a+b/2, c/2)

AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E with coordinates ​(a+b/2, c/2)​

By the definition of midpoint, AE¯¯¯¯¯≅CE¯¯¯¯¯and BE¯¯¯¯¯≅DE¯¯¯¯¯

Step-by-step explanation:

Answer:

2:5

Step-by-step explanation:

cats: dogs

8:20

We can divide each by 4

8/4: 20/4

2:5

Answer:

14

Step-by-step explanation:

Replace with the values

15-1/2(2) = 15-1 = 14

Answer:

14

Step-by-step explanation:

e-1/2f

Let e =15 and f =2

We can substitute these values into the expression

15 - 1/2 (2)

15 - 1

14

Answer:

x=5/2

Step-by-step explanation:

We can use ratios of similar triangles to help solve the problem.

side                    x                       5

--------              = --------------- = ---------------

hypotenuse               4                   8

Using cross products

x*8 = 4 * 5

8x = 20

Divide each side by 8

8x/8 = 20/8

x = 5/2

heres a trick: if you go to desmos.com/calculator you can type in your equation and it will show you it on the graph.

since f(x)=y you can say y=-3x-2 and it will show you!

Answer:

Option D.

Step-by-step explanation:

The given function is

[tex]f(x)=-3^x-2[/tex]

We need to find the graph of given function.

At x=0,

[tex]f(0)=-3^(0)-2=-3[/tex]

Similarly, substitute the different values of x and find the values of y.

Table of values

x                 y

-1             -2.33

0               -3

1                -5

2              -11

3              -29

Plot these ordered pairs on a coordinate plane and connect them by a free hand curve. The graph of given function is is shown below.

Therefore, the correct option is D.

[tex]|n+8|>3\iff n+8>3\ \vee\ n+8<-3\qquad\text{subtract 8 from both sides}\\\\\boxed{n>-5\ \vee\ n<-11}[/tex]

Answer:

     r+5                 r^2+4r-21

-------------- /   --------------------

r^2+5r-14               r-2

         r+5                     r-2

= --------------  x   --------------------

   r^2+5r-14           r^2+4r-21

         r+5                     r-2

= --------------  x   --------------------

   (r+7)(r-2)           (r+7)(r-3)

         r+5                     

= -----------------

   (r+7)^2 (r-3)          

hope it helps

Step-by-step explanation:

Answer:

x= -4 is the axis of symmetry

Step-by-step explanation:

The parabola is written in the form y = a (x-h)^2 +k

The vertex is (h,k) and the axis of symmetry is at x=h.

Given f(x) = 3(x- -4)^2 + 1, the vertex is (-4,1)  so the axis of symmetry is x= -4

Final answer:

The inequality x>5 can be stated as 'x is greater than five,' 'five is less than x,' or 'x exceeds five,' each conveying that the value of x is larger than 5.

Explanation:

There are several ways to express the inequality x > 5 in words. Here are three different expressions:

All these expressions communicate the idea that the value of x is more than 5. When you're working with inequalities, it's important to be familiar with different ways to verbalize them as it can help in understanding and communicating mathematical concepts.

Answer:

Jeff had in the account 3,623.85 after 3 years

Step-by-step explanation:

Investment: p=3,000

Interest: i=6.5%=6.5/100→i=0.065

Time (in years): t=3

A(3)=?

A(t)=p(1+i)^t

t=3→A(3)=p(1+i)^3

Replacing the given values:

A(3)=3,000 (1+0.065)^3

A(3)=3,000 (1.065)^3

A(3)=3,000 (1.207949625)

A(3)=3,623.848875

Rounding to the nearest hundredth:

A(3)=3,623.85

Answer:

The answer is: 1

Step-by-step explanation:  f(1) = -1, so f(-1) must be 1.

The value of the function by using a given table would be, f (- 1) = 0

Hence, option 3 is true.

Given that,

The function to find the value, f (- 1)

Used the concept of function which stated that, A relation between a set of inputs having one output each is called a function.

Now from the given table,

At x = - 5;

f (- 5) = 4

Similarly,

At x = - 1;

f (- 1) = 0

Therefore, the value of function f (- 1) would be 0.

So, Option 3 is true.

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The complete question is shown in the attached image.

Answer:

12(2V -7)

Step-by-step explanation:

Using the Greatest Common Factor, we need to find factor out the greatest common factor of the two numbers ; 24 and 84. That is; the greatest number that can divide 24 and 84

The easiest way to find the greatest common factors is;

1. To first find the factors of each number

2. Find the common factors of the two numbers

3. Find the greatest number among those factors

Factors are number that can divide a number without a remainder.

Factors of 24 are;   1, 2, 3, 6, 8, 12 and 24

Factors  of 84 are; 1, 2, 3, 6, 7, 12, 14, 42 and 84

common factors are the factors that are common between the two numbers. That is; factors we can find in 24 and as well as 84

common factors are;  1, 2, 3, 6, and 12

Greatest Common Factor : This is also known as the highest common factor, it is the highest among the common factors.

Greatest Common Factor is 12.

Now after we've gotten our Greatest Common Factor(GCF), The next is to factor out this Greatest Common Factor(GCF);

24v - 84 =  12(2v - 7)

Therefore, the factored form of 24v - 84 is  12(2v -7)

The factored form of the given expression is 12(2v-7)

Equations are expressions separated by an equal sign

Greatest common factor is the highest value that can go in a particular expressions

Given the expression 24v - 84

Find that factors of both terms

24v = 12 × 2v

84 = 12 × 7

Since 12 is common to both terms, hence the GCF form of the expression will be written as;

24v - 84 = 12(2v - 7)

Hence the factored form of the given expression is 12(2v-7)

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Answer:

Bruh no one has still answered u?!

Step-by-step explanation:

Answer:

Answer??

Step-by-step explanation:

Answer:

25 nautical miles

Step-by-step explanation:

We need to find the rate.  We can do so using the formula, distance = rate * time

d= rt

We know the distance and the time, so we need to solve for the rate

d/t = rate

d= 150 nautical miles

t = 6 hours

d/t = 150 nautical miles /6 hours

rate = 25 nautical miles per hour

So in 1 hour we can go 25 nautical miles

Answer:

25 nautical miles.

Step-by-step explanation:

Givens

Equation

Solution

Answer:

15 inches by 16 inches

OR

1 foot 3 inches by 1 foot four inches

Answer:

His answer is not reasonable.

Step-by-step explanation:

448 rubber bands to make 12 rubber band bottles of the same size.

450 divided by 10  is about 45 rubber band per rubber band bottle.

This is nowhere near the the 116 rubber bands to make a rubber band ball.

If the are about the same size, we should use about the same number of rubber bands.

If he used about 100 rubber bands per rubber band bottle * 12 bottles, that would be about 1200 rubber bands.

Answer:

domain {- 5, 5 }

Step-by-step explanation:

given values in the range, that is values of y then to find the domain equate f(x) to the given values in the range, that is

x + 5 = 0 ⇒ x = - 5

x + 5 = 10 ⇒ x = 10 - 5 = 5

domain is x ∈ { - 5, 5 }

Answer:

647.0625

Step-by-step explanation:

Answer:

(4,-12)

Step-by-step explanation:

The equation of a circle has the following form:

[tex](x-h)^2+(y-k)^2=r^2[/tex] where (h,k) is the center of a circle with radius r.

Our equation is:

[tex](x-4)^2+(y+12)^2=17^2[/tex]

The center is (4,-12).

Answer:

(4,-12)

Step-by-step explanation:

Answer:

1/(11 x^(9/2) y^4 z^5)

or

sqrt(x)/ 11 x^5 y^4 z^5  

Step-by-step explanation:

1/ sqrt(121x^9y^8z^10)

Lets simplify the denominator

sqrt(121x^9y^8z^10)

Break it into pieces

sqrt(121) sqrt(x^9) sqrt(y^8) sqrt(z^10)

11  sqrt (x^8) sqrt(x) y^4  z^5

11 x^4 y^4 z^5  * sqrt(x)  

Putting this back in

1

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

11 x^4 y^4 z^5  * sqrt(x)

But we dont want a sqrt root in the denominator

Multiply by sqrt(x)/sqrt(x)

sqrt(x)

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

11 x^4 y^4 z^5  * sqrt(x) sqrt(x)

sqrt(x)

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

11 x^4 y^4 z^5  * x

sqrt(x)

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

11 x^5 y^4 z^5  

Answer:

n=1.75

Step-by-step explanation:

(7-4n)*6=0

We simplify the equation to the form, which is simple to understand  

(7-4n)*6=0

Reorder the terms in parentheses

(+42-24n)=0  

Remove unnecessary parentheses

+42-24n=0

We move all terms containing n to the left and all other terms to the right.  

-24n=0-42

We simplify left and right side of the equation.  

-24n=-42

We divide both sides of the equation by -24 to get n.  

n=1.75

Answer:

42 - 24n

Step-by-step explanation:

This is an expression, not an equation.  We can simplify

(7-4n)*6

Distribute the 6

7*6 - 4n*6

42 - 24n

Answer:

the answer issss

Step-by-step explanation:

k=60

Answer:

The value of is equal to [tex]k=60\°[/tex]

Step-by-step explanation:

we know that

[tex](2k+11)\°=131\°[/tex] -----> by alternate exterior angles

solve for k

[tex]2k=131\°-11\°[/tex]

[tex]k=120\°/2=60\°[/tex]

Answer:

They are not proportional.

Step-by-step explanation:

To check if the fractions are proportional, we can use cross products.

1                6

----- =  --------------

3                   20

1 * 20  = 3 * 6

20 = 18

This is not true, so they are not proportional.

Answer,

No

Explanation,

To find out if a pair of fractions are proportional you can use cross multiplication. Only fractions that are equivalent to eachother are proportional.

1/3 = 6/20

1 * 20 = 20

3 * 6 = 18

As we can see they are not equivalent, therefore it is not proportional.

Hope This Helps :-)

Riding a bicycle for one hour burns 700 calories. Therefore,  biking for two hours burns a total of 1400 calories.

To solve this question, we need to understand that vacuuming and mopping for an hour burns 280 calories, which is 40% of the calories burned by biking for the same time. The first step is to determine the total number of calories burned when biking for one hour.

Let x represent the total number of calories burned by biking for one hour. According to the problem, 40% of x is 280 calories, which we can write as:

0.40x = 280 calories

To find the value of x, we divide both sides of the equation by 0.40:

x = 280 / 0.40

x = 700 calories

Thus, biking for one hour burns 700 calories. Now to find out the total number of calories burned by biking for two hours, we simply multiply this number by 2:

Total calories for 2 hours of biking = 700 calories × 2

Total calories for 2 hours of biking = 1400 calories

The answer is that riding the bicycle for two hours burns a total of 1400 calories.

Answer:

The length of the rectangle is 17 cm and the width of the rectangle is 5 cm.

Step-by-step explanation:

Given the measurements in the question, you can set up two different equations to find the length and width of the rectangle.  First, the formula for the perimeter of a rectangle is:  P = 2W + 2L, where W = width and L=length.  In this problem the L is '7 more than twice its width', this means our first equation is:

L = 2W + 7

Next, we can use this expression in our formula for perimeter to get our second equation:

P = 2W + 2(2W + 7)  or 44 = 2W + 2(2W + 7)

Distribute:  44 = 2W + 4W + 14

Combine like terms:  44 = 6W + 14

Subtract 14 from both sides:  44 - 14 = 6W + 14 - 14 or 30 = 6W

Divide 6 from both sides:  30/6 = 6W/6 or W = 5

Now, solve for L:  L = 2(5) + 7 or L = 10 + 7 = 17

So, the width is 5cm and the length is 17 cm.

The length of the rectangle is 17 cm and the width of the rectangle is 5 cm

The area of Rectangle is length times of width.

Given that perimeter of a rectangle is 44 cm.

Its length is 7 more than twice its width.

Length=2w+7

Width=w

Perimeter=2(Length+Breadth)

44=2(2w+7)+2w

Apply distributive property on right hand side

44=4w+14+2w

44=6w+14

Subtract 14 on both sides

30=6w

Divide both sides by 5

5=w

So width of rectangle is 6cm and length is 2(5)+7=10+7=17 cm

Hence, the length of the rectangle is 17 cm and the width of the rectangle is 5 cm

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Answer:

12 days

Step-by-step explanation:

Time taken by one man = x days , and that by 1 boy = y days

work done in 1 day by one man = 1/x

work done in 1 day by one boy= 1/y

work done by 2 men in one day = 2/x

work done by 7 boys in one day = 7/y

2/x + 7/y = 1/4      -----> [ 1]

work done by 4 men in one day = 4/x

work done by 4 boys in one day = 4/y

4/x + 4/y = 1/3       ----> [2]

Multiplying  equation 1 by  , 2 ,  

2(2/x + 7/y = 1/4   )

 = 4/x + 14/y = 1/2           ---> [3]

solving equations 2 and 3

 4/x + 4/y = 1/3  

- 4/x + 14/y = 1/2  

==============

-10/y = 2-3/6

-10/y = -1/6

-1/6y = -10

y = -10 × 6/-1

  = 60 

2/x + 7/y = 1/4

2/x + 7/60 = 1/4

7/60 - 1/4 = -2/x

-8/60 = -2/x

-120 = -8x

x = -120/-8

x = 15

=================================

Time taken by 1 man to do the  whole job = 15 days

time taken by 1 boy to do the whole  job = 60 days

time taken by one boy and one man to do one day's work = 1/60 + 1/15

                                         = 1/60 + 4/60

                                         = 5/60  = 1/12

Together they can do it in 12 days !

Answer:

A= 40

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3/4 (2a-6)+1/2=2/5(3a+20)

(3/4) (2a) + (3/4) (-6) + 1/2 = (3a) + (2/5) (20)

(distribute)

3/2a + -9/2 + 1/2 = 6/5a + 8

(3/2 a) + ( -9/2 + 1/2 ) = 6/5a + 8 (Combine like terms)

3/2a + -4 = 6/5a + 8

3/2a -4 = 6/5a+8

Step 2: Subtract 6/5a from both sides.

3/2a - 4 - 6/5 a = 6/5a + 8 - 6/5 a

3/10 a - 4= 8

Step 3: Add 4 to both sides.

3/10a -4 +4 = 8 + 4

3/10 a = 12

Step 4: Multiply both sides by 10/3

(10/3) * (3/10a) = (10/3) * (12)

a = 40

Answer:

40

Step-by-step explanation:

Answer:

[tex]\frac{12}{5}[/tex]

Step-by-step explanation:

First, we need to find the gradient (slope) of the FG line.

To do this we must use the gradient formula:

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

y1 and x1 have to be in the same coordinate set,

x1 = 8, y1 = 4   the (8 , 4) set

x2 = -4, y2 = 9   the (-4 , 9) set

[tex]\frac{9 - 4}{-4 - 8}[/tex]

[tex]\frac{5}{-12}[/tex]

Which is the gradient of FG line.

To find the equation of a line perpendicular to this line, you must do [tex]\frac{-1}{gradient}[/tex]

[tex]\frac{-1}{\frac{5}{-12} }[/tex]

= [tex]\frac{12}{5}[/tex]

So that means the gradient of the line perpendicular to FG is

[tex]\frac{12}{5}[/tex]

change in velocity = 20 - 0 = 20

change in time = 2 seconds

Divide the change in velocity over the change in time: 20/2 = 10

The average acceleration is 10 m/s^2

I.e, each second, the speed increases by 10 m/s

Runner's average acceleration was 10 m / s²

The average acceleration refers to how fast the runner is going in relation to time.

It is calculated by the formula:

= Change in speed / Time

Change in distance here is:

= 20 m/s - 0 m/s

= 20 m/s

The acceleration is therefore:

= 20 / 2

= 10 m/s²

In conclusion, the runner was accelerating at a rate of 10 m/s².

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