5. Standard form of 15240000 is :

The total number of laps Sarah should run today is given by the equation A = 16 laps

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of laps be represented as A

Now , the equation will be

The total distance ran by Sarah yesterday = 3,682 m

The distance of one lap = 263 m

So , the number of laps ran by Sarah yesterday = total distance ran by Sarah yesterday / distance of one lap

Substituting the values in the equation , we get

The number of laps ran by Sarah yesterday = 3682 / 263

The number of laps ran by Sarah yesterday = 14 laps

Now ,

The distance Sarah wants to run today = 4,222 m

So , the number of laps Sarah should run today A = distance Sarah wants to run today / distance of one lap

Substituting the values in the equation , we get

The number of laps Sarah should run today A = 4,222 / 263

The number of laps Sarah should run today A = 16.05 laps

The number of laps Sarah should run today A = 16 laps

Therefore , the value of A is 16 laps

Hence , the number of laps is 16 laps

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The expression 14x⁴y³ - 42x³y⁴ is rewritten to 14x³y³(x - y)

An algebraic expression can be described as a mathematical expression that is made up of terms, coefficients, variables, factors and constants.

They are also made up of some arithmetic operations, such as;

From the information given, we have the algebraic expression;

14x⁴y³ - 42x³y⁴

Now, factor the common numbers, we have;

14(x⁴y³ - 3x³y⁴)

Factor the common variables, we get;

14x³y³(x - y)

Hence, the expression is 14x³y³(x - y)

Learn more about algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

The fourth point is (-6.5, -14)

Vertices of a parallelogram?

The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.

The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.

One way to find the fourth vertex is to use the vector that connects one vertex to another. The vector from (-7,-6) to (6,3) is (13,9), and from (6,3) to (4,-4) is (-2,-7)

If we use the vector which is opposite of (-2,-7) that is (2,7) and add it to the third point (4,-4) , we will get the fourth point.

(2,7) + (4,-4) = (6,3)

so the fourth point is (6,3)

Another way is to find the midpoint of the diagonal of the parallelogram which are (-7,-6) and (4,-4) and then add the vector which is opposite of (6,3) to (4,-4) that is (-6,-9) which is also the vector from (6,3) to (4,-4)

Midpoint of (-7,-6) and (4,-4) = (-0.5,-5)

(-0.5,-5) + (-6,-9) = (-6.5, -14)

Hence, the fourth point is (-6.5, -14)

To learn more about parallelogram, Visit

https://brainly.com/question/970600

#SPJ1

Answer:

6 chairs

Step-by-step explanation:

The break even Point on gaming chairs can be expressed as :

Revenue = Cost

Revenue, R = 50x

Cost, C = 30x + 120

R = C

50x = 30x + 120

50 - 30x = 120

20x = 120

Divide both sides by 20

20x/ 20 = 120 / 20

x = 6

Hence, 6 chairs must be sold for the company to break even.

Answer:

u can use formula whole root ,( x2-x1)²+(y2-y1)²

hope it helps...

Answer:

7.8 (1.d.p) or √61

Step-by-step explanation:

To solve this question we must use Pythagoras (a²+b²=c²)

Imagine that the line given is the hypotenuse (the longest side of a right-angled triangle) of a right-angled triangle and the other sides as a line from B going to the right, and a line from A going downwards (making the final vertexes for the triangle at coordinates: (3,2), which is B,  (9,7), which is A, (9,2), which is the vertex the 2 imaginary lines we added, created) So now we use Pythagoras to find the length of the hypotenuse:

9-3=6 (subtracting the xs of vertexes A and B to find the length of the imaginary line we extended from B) and

7-2=5 (subtracting the ys of vertexes A and B to find the length of the imaginary line we extended from A)

Now to put them into Pythagoras's formula:

6²+5²=c² ⇒ 36+25=c² ⇒ √36+25=c ⇒ √61 = c ⇒ c = 7.8102....

Which can be rounded to 7.8 (as the third digit, the 1, rounds down.

Answer:

sry i thought i knew how to do it but I can't remember

Step-by-step explanation:

Answer:

(x + 5)² + 10

Step-by-step explanation:

Given

x² + 10x + 35

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 10x

x² + 2(5)x + 25 - 25 + 35

= (x + 5)² + 10

Answer:

looool

Step-by-step explanation:

Answer:

m∠ABC = 55°

Step-by-step explanation:

m∠BAC = 50° because ∡BAC ≅ ∡DCA

since there are 180° in ΔABC the m∠ABC = 180-(75+50) which equals 55°

Answer:

See below

Step-by-step explanation:

This is a parabola in vertex form where the vertex is (-2,7) and the parabola is vertically compressed by a factor of 3.

Alex is standing somewhere in between Gina and Dana. Thus, the least possible number of people between Dana and Alex are:

20.

In advanced mathematics, the number line can be called as a real line or real number line, formally defined as the set R of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one.

A number line is useful because it acts as a visual math aid. It can support teachers and parents as they teach children how to count and write numbers. It's also a tool that can help build understanding behind adding, subtracting, multiplying, and dividing numbers.

Let's assume that Gina is standing on first number while Dana on the last. Hence the total number of people in the line are: n= 23.Alex is standing somewhere in between Gina and Dana. Thus, the least possible number of people between Dana and Alex are: (n-2) = 20.

To learn more about number line visit:

https://brainly.com/question/13425491

#SPJ4

Yes the statement is true.

An object is enlarged if the scale factor is greater than 1. An object is reduced if the scale factor is a fraction, less than 1. A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.

Given here Absolute value of the scale factor is greater than 1

∴ The  object is enlarged if the scale factor is greater than 1.

Hence, Yes the statement is true.

Learn more about Dilations here:

https://brainly.com/question/13176891

#SPJ1

Since you're feeding it three times a day, you should feed your goat 0.74 ounces per feeding.

The act of feeding involves giving a baby a mother's breast milk, either directly from the breast or by expressing (pump-out) the milk from the breast and giving it to the baby in a bottle.

In the traditional method of measurement, a pound is used to measure weight. In the conventional system, ounces are smaller weight units that are defined in terms of pounds. 1 pound Equals 16 ounces.

Goats typically need around 2% to 4% of their body weight in feed per day. If your goat weighs 7 pounds, and you want to feed it 2% of its body weight per day, you would need to feed it 0.14 pounds of food per day, or 2.24 ounces per day. Since you're feeding it three times a day, you should feed it 0.74 ounces per feeding.

To learn more about Ounce visit:

https://brainly.com/question/29374025

#SPJ1

In Week 1,

Salesman C got larger paycheck than Salesman A and Salesman B.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable. That means, the equation 2x – 5 = 13 is satisfied only for x = 9.

Given,

Commission of salesman A per sale = $65

Commission of salesman B per sale = $40

Commission of salesman C per sale = $0

Salary of salesman A per week = $0

Salary of salesman B per week = $300

Salary of salesman C per week = $900

No. of sales × commission + salary = total earning

In week 1.

Earning of A

11 × $65 + $0 = $715

Earning of B

14 × $40 + $300 = $860

Earning of C

16 ×$0 + $900 = $900

In week 2.

Earning of A

14 × $65 + $0 = $910

Earning of B

15 × $40 + $300 = $900

Earning of C

12 ×$0 + $900 = $900

In week 3.

Earning of A

16 × $65 + $0 = $1040

Earning of B

13 × $40 + $300 = $820

Earning of C

111 ×$0 + $900 = $900

By the above calculation Salesman C received $900 in week 1 which is greater than Salesman A and Salesman B.

In week 2 and week 3 his paycheck is smaller than both of the other salesman.

Hence, Salesman C  received larger paycheck than both of the other salesmen in Week 1.

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ1

its a virus dont  fall for it

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

a^2=b(b+c)

12^2=8(8+x)

144=64+8x

-64 -64

______

80=8x

x=10

The given problem has been proved below using the rules of Congruence.

The given problem can be solved easily if we apply the basic rules of Congruence on the question properly as they are required. Congruence is when two given figures have the same shape and size.

Given that,

3AB=7AD

3AC=7AE

So, by re-arranging them we get the same ratio that is,

AB/AD=7/3

AC/AE=7/3

Hence, we can conclude that,

AB/AD=AC/AE

Also, we can show that ∠BAC and ∠DAE by the property of vertical angles.

But ∠BAC ≌ ∠DAE is also true by the vertical angle theorem in this diagram.

So, SAS property ∆ABC~∆ADE is proved in the end.

Learn more about Congruence on

https://brainly.com/question/30105362?referrer=searchResults

#SPJ4

Answer:

b.

Step-by-step explanation:

Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , 5) and a "p" distance of negative 2 units, since it's opening to the left, so

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=5\\ p=-2 \end{cases}\implies 4(-2)(~~x-0~~) = (~~y-5~~)^2\implies {\Large \begin{array}{llll} -8x=(y-5)^2 \end{array}}[/tex]

Answer:

17

Step-by-step explanation:

A right triangle with congruent legs and acute angles is an Isosceles Right Triangle.

A special right triangle is a right triangle that has a consistent characteristic that facilitates calculations on the triangle or for which straightforward formulas are available.

Angles in a right triangle, for instance, might create straightforward connections like 45°-45°-90°. An "angle-based" right triangle is what this is. When the side lengths of a right triangle form ratios of whole numbers, such as 3:4:5, or other unusual numbers, like the golden ratio, the triangle is said to be "side-based."

Without using more complex techniques, one can rapidly determine different lengths in geometric problems by understanding the relationships between the angles or side ratios of certain particular right triangles.

Learn more about the Triangles here;

brainly.com/question/30108144

#SPJ4

The inequality to find the cost of the pizza they should order is c ≤ 14. The cost is at most $14.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Trey and three of his friends are ordering a pizza and they want to spend at most $3.50 per person. An inequality to find the cost of the pizza they can order is:

c ≤ (3.50 × 4)

c ≤ 14

The cost will be at most $14.

Learn more about inequalities on:

brainly.com/question/24372553

#SPJ1

Driving from North Carolina to Florida at an average speed of 70 mph takes about 7 hours and 12 minutes.

Velocity is a term used to describe how fast an object is moving in a particular direction. It is measured as distance traveled in a period of time and is usually expressed in units of meters per second (m/s). Velocity is an important concept in physics and is used to calculate how fast an object moves in a given environment. Velocity is related to speed, which is the rate of change of distance in a particular direction. Speed ​​is an important factor in many sports and activities such as running, cycling and driving. It is also used in different ways in our daily life. For example, it is used to determine how fast a car can go from A to B, or how long it will take to walk to a destination.

Speed = Distance/Time

55 = Distance/9

Distance = 495 miles

When speed is 70 mph:

70 = 495/Time

Time = 495/70

Time = 7 hours and 12 minutes

To know more about speed click-

https://brainly.com/question/13943409

#SPJ1

Answer:

< 1 = 125 degrees

< 2 = 55 degrees

< 3 = 125 degrees

< 4 = 55 degrees

< 5 = 125 degrees

< 6 = 55 degrees

< 7 = 125 degrees (given)

< 8 = 55 degrees

Step-by-step explanation:

1 and 3 are equal because they are vertical angles, therefore proving their congruence.

7 and 1 are equal because they're alternate exterior angles, which are congruent.

2 and 4 are vertical, which is congruent.

5 and 7 are vertical.

6 and 8 are vertical.

Answer:

1) Yes

2) No

3) Yes

4) Yes

Step-by-step explanation:

Remember the rule: the sum of the two shortest sides must be bigger than the longest side. From there, the answers should be obvious. Just add up the smallest sides for each triplet of lengths and see if that is bigger than the largest side.

7 + 14 > 18, therefore this can be a triangle

3 + 8 < 17, therefore this can't be a triangle

3.2 + 9.0 > 11.5, therefore this can be a triangle

6 + 7 > 8, therefore this can be a triangle

Answer:660,000

Step-by-step explanation:

principle= 24,000

rate=5.5%

time = 5years

simple interest= P×R×T

. =24000×5.5×5

. = 660,000

The Diwali occurred on 0.408 or 40.8% of the year in 2017.

To find the fraction of the year that Diwali occurred in 2017, we need to divide the number of days between Diwali and the start of the year by the total number of days in the year.

Diwali occurred on Thursday, October 19, 2017. The start of the year 2017 is January 1, 2017 which is a Sunday.

There are 365 days in a non-leap year. Since 2017 is not a leap year, there are 365 days in that year.

So the fraction of the year that Diwali occurred in 2017 can be calculated as: (days between Diwali and the start of the year) / (total days in the year) = ( 19 + 31 + 30 + 31 + 30 + 19 ) / 365 = (148) / 365 = 0.408

So, the Diwali occurred on 0.408 or 40.8% of the year in 2017.

Therefore, Diwali occurred on 0.408 or 40.8%

To learn more about fractions,

Visit; brainly.com/question/10354322

#SPJ4

Answer:

11.5

Step-by-step explanation: