Sum of first 1000 consecutive odd counting numbers

Answer:

???

Step-by-step explanation:

Where's the problem/question?

Answer:

The flower garden width would be 6 ft

Step-by-step explanation:

A = 12 ft^2 = x(x + 4) becomes:

x^2 + 4x - 12 = 0, or (by completing the square) x^2 + 4x + 4 - 4 - 12 = 0

Thus, we have (x + 2)^2 - 16 = 0, or (x + 2)^2 = 16

Taking the square root of both sides yields x + 2 = ±4.

In this context only a positive x value makes sense:  x = 2 + 4  =>  x = 6.

The flower garden width would be 6 ft.  The other dimension would be 6 - 4, or 2, ft.

To find the width of the flower garden when the area is 12 square feet, the equation A = x(x-4) is used. Solving for x, the width of the flower garden is 6 feet.

To find the width of the flower garden when the area is 12 square feet:

Plug in A=12 into the equation: 12 = x(x-4)

Solve the equation for x by factoring or using the quadratic formula

The possible values for x are 6 and -2, but since width can't be negative, the width of the flower garden is 6 feet (B)

Answer:

[tex]d=5t+20[/tex]

Step-by-step explanation:

The equation that will model this situation will be of the form

[tex]d=mt+b[/tex]

where [tex]t[/tex] is the time in hours john has traveled since the gas station, and  [tex]d[/tex] is the distance.

Now we know that John has already traveled 20 miles when he is at the gas station, this means at [tex]t=0[/tex], [tex]d=20[/tex]; or

[tex]20=m(0)+b[/tex]

[tex]\boxed{b=20}[/tex]

Thus we have

[tex]d=mt+20[/tex].

Now we need to figure out [tex]m.[/tex]

When John reaches home 2 hours later he notes that he has traveled 30 miles, which means he has traveled 30 - 20 = 10 miles; thus we have

[tex]m= \frac{\Delta d}{\Delta t} =\frac{10 miles}{2hours} =5[/tex]

[tex]\boxed{m=5}[/tex]

Now we have the full equation:

[tex]\boxed{d=5t+20}[/tex]

We can multiply first equation x + 3y = -14 by 2 to get rid of varibale "x"

Solution:

Given that, the system of equations are:

x + 3y = -14 ----- eqn 1

2x + y = -3 --------- eqn 2

We can solve by elimination method

For doing elimination, we have to make the any one of coefficient of variable same

Here, in eqn 1 we have 1 as coefficient for "x"

In eqn 2, we have 2 as coeficient for "x"

So, we can multiply eqn 1 by 2, to get rid of "x"

2(x + 3y = -14)

2x + 6y = -28 ------- eqn 3

If we subtract eqn 2 from eqn 3, we will get the solution

2x + 6y = -28

2x + y = -3

( - ) ----------------

5y = -25

Substitute y = -5 in eqn 1

x + 3(-5) = -14

x -15 = -14

Thus the solution is x = 1 and y = -5. So we have multiplied equation 1 by 2 to get of varibale "x" and solved the equations

Answer:

  D.  123.9 - 20.886x

Step-by-step explanation:

Using the distributive property, we find the expansion to be ...

  5.9(21) +5.9(-3.54x) = 123.9 -20.886x

_____

The distributive property tells you ...

  a(b+c) = ab +ac

The factor outside parentheses multiplies each of the individual terms inside parentheses.

Answer:

20+4x

Step-by-step explanation:

Distributive property is quite easy to learn... its just multiplication in an easier form to visualize once you're used to using it.

To first start this problem you want to use the number 4 in the expression 4(5+x). You then want to multiply 4 by both terms inside of the parentheses. So you would do both 4*5 and 4*x. You would then get 20+4x because 4*5=20 and 4*x is just put together as 4x.

Answer:

[tex]4(5+x)=20+4.x[/tex]

Step-by-step explanation:

Distributive property:-

The distributive property is one of the most frequently used properties in mathematics.

Distributive property

a(b+c) = a.b+a.c ((using multiplication of distributive law)

given

[tex]4(5+x) = 4.5+4.x[/tex]

[tex]4(5+x)=20+4.x[/tex]

Answer:

Krutika get 21

Alex get 21

Gordon get 7

Step-by-step explanation:

Given: Total amount= 49

           Ratio= 3:3:1

Now, finding the amount received by Krutika, Alex and Gordon.

First, lets find the sum of ratio

Sum of ratio= [tex]3+3+1= 7[/tex]

We know now that amount will be distributed in the following fraction:

Krutika= [tex]\frac{3}{7}[/tex]

Alex= [tex]\frac{3}{7}[/tex]

Gordon= [tex]\frac{1}{7}[/tex]

∴ Amount received by Krutika= [tex]\frac{3}{7}\times 49= 21[/tex]

Alex,

Amount received by Alex= [tex]\frac{3}{7}\times 49= 21[/tex]

Gordon,

Amount received by Gordon= [tex]\frac{1}{7}\times 49= 7[/tex]

Hence, they get 21,21 and 7 respectively out of 49.

KKrutika and Alex each get £21, and Gordon gets £7.

To find out how much money each person gets, you need to divide the total amount of money (£49) in the ratio of 3:3:1.

First, add up the parts of the ratio to find the total number of parts: 3 + 3 + 1 = 7.  

Next, divide the total amount of money (£49) by the total number of parts (7) to find the value of one part: £49 ÷ 7 = £7.  

Finally, multiply the value of one part (£7) by each part of the ratio to find out how much money each person gets: KKrutika and Alex each get £7 × 3 = £21, and Gordon gets £7 × 1 = £7.

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Answer:

y equals 45, because you substitute the x in the bigger equation with -2, and then solve for y

There are 43 nickels in the piggy bank.

Step-by-step explanation:

Given,

Amount in piggy bank = $6.95 = 6.95*100 = 695 cents

Total coins = 91

One nickel = 5 cents

One dime = 10 cents

Let,

x be the number of nickels

y be the number of dimes

According to given statement;

x+y=91          Eqn 1

5x+10y=695    Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=91)\\10x+10y=910\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](10x+10y)-(5x+10y)=910-695\\10x+10y-5x-10y=215\\5x=215[/tex]

Dividing both sides by 5

[tex]\frac{5x}{5}=\frac{215}{5}\\x=43[/tex]

There are 43 nickels in the piggy bank.

Keywords: linear equation, elimination method

Learn more about linear equations at:

#LearnwithBrainly

Final answer:

To find the number of nickels in the piggy bank, you can set up a system of equations. By solving the system, it is determined that there are 43 nickels.

Explanation:

To find the number of nickels in the piggy bank, we need to set up a system of equations. Let's assume that the number of nickels is 'x' and the number of dimes is 'y'.

We know that there are a total of 91 coins, so we can write the equation: x + y = 91.

We also know that the value of the nickels is 5 cents and the value of the dimes is 10 cents. The total value of the coins is $6.95, so we can write the equation: 5x + 10y = 695.

Solving this system of equations will give us the number of nickels.

First, let's multiply the first equation by 5 to eliminate 'x'.

5x + 5y = 455

Next, subtract this new equation from the second equation.

(5x + 10y) - (5x + 5y) = 695 - 455

5y = 240

y = 48

Finally, substitute the value of 'y' back into the first equation to find 'x'.

x + 48 = 91

x = 43

Therefore, there are 43 nickels in the piggy bank.

Final answer:

The equation representing the total cost for an adult and five children renting skates, with the adult's rental at $4 and the total at $16, is 4 + 5x = 16.

Explanation:

The question is asking for an equation that represents the total cost for an adult and five children renting skates where the adult's rental costs $4 and the total cost is $16. To write this equation, we let x be the cost for renting skates for a child. Since there are five children, the cost for the children's skates is 5x. Adding the adult's cost, we have the total cost expressed as 4 + 5x = 16.

Explanation: We know that the cost for one adult is $4, so that's a fixed amount. Since we don't know the individual cost for a child's skate rental, that's our variable x. We have five children, so we multiply x by 5. Adding up the adult's cost and the children's cost gives us the total cost, which is $16, and thus we arrive at our final answer, 4 + 5x = 16.

Answer:

He have 0.96 acres of early corn.

Step-by-step explanation:

Given:

Toms garden is 8 acres. Two fifths is corn.

Of that, three tenths is early corn and one tenth is late corn.

Now, to find the acres of early corn.

Total garden = 8 acres.

Total Corn in garden = [tex]\frac{2}{5}\ of\ 8=\frac{2}{5} \times 8=\frac{16}{5}[/tex] acres.

As, given of the total corn in garden, three tenths is early corn.

Now, to get the early corn he have:

= [tex]\frac{3}{10} of \frac{16}{5}[/tex]

= [tex]\frac{3}{10} \times \frac{16}{5}[/tex]

= [tex]\frac{48}{50}[/tex]

= [tex]0.96\ acres.[/tex]

Therefore, he have 0.96 acres of early corn.

Answer:875 feet

350÷2=175

350+350+175=875

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Final answer:

To solve these physics problems, we used vector mathematics to find the speed of the ball, its position after a certain time, the time it aligns with a certain point, and the speed of a player to intercept it. Additionally, we considered gravity as a factor for a more realistic model of the ball's motion.

Explanation:

Speed of the ball: To find the speed of the ball, we calculate the magnitude of the velocity vector (5i + 8j) m/s using the Pythagorean theorem, which results in \(\sqrt{5^2 + 8^2} = \sqrt{89}\) m/s.

Position vector after t seconds: We calculate the position vector at time t by using the initial position vector (2i + j) m and adding the product of the velocity vector and time t. This yields the formula (2i + j) + t(5i + 8j).

Time when the ball is due north of B: For the ball to be due north of B, their i-components must be equal. Given B's position vector is (10i + 7j), we set the i-component equal to 10 and solve for t, getting t = (10 - 2)/5 = 1.6 seconds.

Value of v for the running player: Since the player intercepts the ball after 1.6 seconds, and the ball's j-component of the velocity is 8 m/s, the player's velocity v must be the distance covered in the j direction divided by time, which is (8j - 7j)/1.6 = 0.625 m/s.

Physical factor for a more realistic model: One physical factor to make the model more realistic could be the effect of gravity on the ball's trajectory, which would cause the ball to follow a parabolic path rather than a straight line.

Answer:

111

Step-by-step explanation:

So firstly, you have two t-shirts, so you do 15.22*2=30.44. Then you use 67.94, and subtract 30.44, which is 37.5

Simple as that!!

Answer:

5 multiple choice questions

Step-by-step explanation:

Write equations to represent the situation.

let "x" be the number of multiple choice questions

let "y" be the number of short answer questions

Equation for the total number of questions:

x + y = 20        # of multiple choice questions + # of short answer questions

Equation for the total points: (Multiply the type of question with how many points you get.)

x + 3y = 50     You don't need to write '1' beside 'x' for multiplying by 1.

The system of equations we need to solve is:

x + y = 20 and x + 3y = 50

We can solve using the substitution method.

Rearrange x + y = 20 to isolate one variable.

Isolate 'y'.

x + y = 20

x - x + y = 20 - x     Subtract 'x' from both sides

y = 20 - x

Take the other equation x + 3y = 50. You can replace 'y' with the equation that equals 'y' that we got when rearranging.

Substitute y for 20 - x

x + 3y = 50

x + 3(20 - x) = 50    Use distributive property. Multiply the 3 outside the bracket by each number inside the bracket.

x + 60 - 3x = 50     Combine like terms. 'x' and '-3x' are alike because they both have 'x'.

60 - 2x = 50          Start isolating 'x'.

60 - 60 - 2x = 50 - 60     Subtract 60 from both sides.

-2x = 50 - 60     60-60 cancels out on the left side.

-2x = -10

-2x/-2 = -10/-2       Divide both sides by -2 to isolate 'x'.

x = -10/-2           -2x/-2 becomes 'x'. -2/-2 cancels out.

x = 5          Number of multiple choice questions

Therefore there are 5 multiple choice questions.

If you needed the number of short answer questions too, you would substitute x for 5 in any of the other equations.

Answer:

9

Step-by-step explanation:

The way to find the answer is by finding the point we're the two circles intersect and adding the number in that space to the number in the middle as the people in the middle are shown to be capable of both things as well

Answer:

their sum: 2.8m

their difference: 1.2m

the third side's length should be smaller than their sum, larger than their difference

it could be: 1.3-1.4-1.5-1.6-1.7-1.8-1.9-2-2.1-2.2-2.3-2.4-2.5-2.6-2.7 but since it has to be a whole number, 2m is the only eligible answer.

Using the Pythagorean theorem, we can calculate the third side of the triangle considering both positions for the side: as the hypotenuse and one of the two remaining sides. In both cases, the result is rounded to a whole number due to the constraints of the question.

In this case, we need to calculate the third side of the triangle based on the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides, which can be written as: a² + b² = c². To find the possible lengths of the third side, we need to consider that it should be a whole number, and use both possible positions: once as a hypotenuse and once as the other side of the triangle.

If the third side is the longest (hypotenuse), then based on the Pythagorean theorem: (1.9m)² + (0.7m)² = c². The answer should be rounded to a whole number.

If the third side is not the longest one, then we could subtract the square of the shorter side from the square of the longer one: (1.9m)² - (0.7m)² = (c)². Again, the answer should be rounded to a whole number.

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Answer:

x = 12

Step-by-step explanation:

1. Set up a proportion:

32             (32 + x)

------   =      ------------

24             (24 + 9)

2. Cross-multiply & solve for x:

32*(24 + 9)    =     24*(32 + x)

1056     =     768 + 24x

288      =      24x

    12     =       x

    x     =   12

Answer:

The equivalent expression can be given as:

⇒  [tex]2t-3q[/tex]

Step-by-step explanation:

Given expression:

[tex]-3t+4q+5t-7q[/tex]

To write an equivalent expression:

Solution:

In order to write an equivalent expression, we will combine the like terms. By like terms, we mean the terms with the same variable constant.

For example : [tex]5x[/tex] and [tex]-3x[/tex]  are like terms.

We have:

[tex]-3t+4q+5t-7q[/tex]

Combining like terms :

⇒ [tex]-3t+5t+4q-7q[/tex]

⇒  [tex]2t-3q[/tex]

Thus, the equivalent expression can be given as:

⇒  [tex]2t-3q[/tex]

Answer:

-7/12

Step-by-step explanation:

An equation can be made out of this problem.

Sum means adding, so in this problem, you are adding 7 to the product of x and 12.

Product means multiplying, so you are multiplying x by twelve to get 12x.

Since you are adding all of this to 7, you get the equation 7 + 12x = 0.

Now, you just need to solve for x by subtracting the 7 over, giving you 12x = -7.

Now, to isolate x, divide both sides by 12. The twelves on the left cancel each other out, leaving you with -7/12.

Answer:

720$

Step-by-step explanation:

(1000+(230*24))-5800=720

Answer:

False

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b

where m is the slope and c the y- intercept

She had 100 points then lost 12-0 points.

Subtract 120 from 100.

100 - 120 = -20

Answer:20

Step-by-step explanation:

Answer:

Data;

1) Line P to Q can be represented as

[tex]--\\PQ[/tex]

2)

The Line P, Q and R will be represented as

[tex]PQ + QR = PR[/tex]

3)

The point P and Q will be represented as

[tex]< \to \\PQ[/tex]

With the sign above it's head

4)

point P will be represented as

[tex].P[/tex]

5)

The point PQ moving towards in the right hand side can be represented as

[tex]\to\\PQ[/tex]

Learn more on lines and points here;

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Answer:

16 lamps

Step-by-step explanation:

we know that

96 lamps represent the 100%

so

using proportion

Find out how many lamps represent 16 2/3%

but first convert to an improper fraction

[tex]16\frac{2}{3}\%=\frac{16*3+2}{3}=\frac{50}{3}\%[/tex]

Apply proportion

[tex]\frac{96}{100\%}=\frac{x}{\frac{50}{3}\%} \\\\x= (\frac{50}{3})(96)/100\\\\x=16[/tex]

Answer:

16 lamps

Step-by-step explanation:

Answer:

Step-by-step explanation:

15/45 = 1/3  {giving by 15th table}

        = 0.33

Answer:

Yes

Step-by-step explanation: 2/8 is eq equivalent to 1/4 when reduced to the lowest term(i.e form)

Yes, this is because 2/8 is equivalent to one fourth, this is because eighths are fourths cut in half, so, you only need two of them to make a one right.

Hope this helps, if not, comment below please!!!