Determine the value of x.
3
6
3√2
3√3

The distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.

The distance between the line ax +by +c =0 and the point (x₁, y₁) is given by:

[tex]d=\frac{|ax_{1}+by_{1}+c|}{\sqrt{a^2+b^2}}[/tex]

Given that, the line passes through the points (0,-3) and (7,4).

The equation of the line is given by:

[tex]y -(-3)=\frac{4-(-3)}{7-0}(x-0)\\\\y+3=x\\\\x-y-3=0[/tex]

Now, the distance between the line x - y - 3 = 0 and point (4,3) is:
[tex]d=\frac{|1\times4+(-1)\times3+(-3)|}{\sqrt{1^2 +(-1)^2}}\\\\d=\frac{2}{\sqrt{2}}\\\\d=\sqrt{2}[/tex]

Hence, the distance between the line containing the points (0,-3) and (7,4) and the point P(4,3) is d =√2 units.

Learn more about the distance between a line and a point:
https://brainly.com/question/11558698

#SPJ1

Answer:

y+3x=-16

Step-by-step explanation:

y=mx+c

y=-3x+c

-3x is the gradient

-5 is the x value and -1 is the y value

-1=-3x-5+c

-1=15+c

-16=c

y=-3x-16

y+3x=-16

Using the formula of compound interest, the amount accumulated over 4 years is $15,849.46

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period. In Mathematics, compound interest is usually denoted by C.I.

The formula is often given as;

C.I = P(1 + r/n)^nt

Substituting the values into the formula

C.I = 200(1 + 0.0105/12)^12*4

However, over the period of 4 years, the Principal becomes

Principal = 200 * 4 * 12 = 9600

Rate = 1.05 * 12 = 12.6

C.I = 9600(1 + 12.6/12)^12 * 4

C.I = $15,849.46

Learn more on compound interest here;

https://brainly.com/question/25297315

#SPJ1

Answer:

I'll try here: 23

Step-by-step explanation:

X = Sam's age.

X-10 = Ted's age

   X + X -10 = 56

    2X -10 =56

    2x = 66

      X = 33 , Sam's age

      33 - 10 = 23  Ted's age

Answer:

Lie #3

b^6 is not b^8

Step-by-step explanation:

All the problems use the quotient rule of exponents, which says that you subtract the exponents when dividing by the same base.

If we plug in 2 for x on #3, we have

[tex]\frac{b^8}{b^2}=b^(^8^-^2^)=b^6\\ b^6\neq b^8[/tex]

Furthermore, x would need to be 0 to make #3 true since 8-0 = 8

Answer:

180

Explanation:

5% of x = 9

9 × 100 = 900

900 ÷ 5 = 180

So,

5% of 180 = 9

5Answer:

45

Step-by-step explanation:

9x0.5=4.5

This is an example of a seasonal component in a time series. A seasonal component refers to regular, predictable patterns that are associated with the time of year, such as increased sales during the summer months.

Selling products or services to clients in exchange for cash or other types of payment is known as ale. The sales process consists of a number of elements, such as:

Product: The items or services being sold are referred to here. A corporation must have a comprehensive grasp of its product offerings and how they fit the demands of its target market.

Price: The sum of money that a consumer must fork over in order to purchase the item or service. Price should be set to maximise profit while maintaining market competitiveness.

Locations where higher the good or service is sold are referred to here as "place." Physical storefronts, internet marketplaces, or a network of distributors may all fall under this category.

To learn more about different components in sales, visit:

https://brainly.com/question/14570921

#SPJ4

Step-by-step explanation:

225 km travels in =25 ltr

1 km travel = 225 25

540 km will require = 22525 ×540=60 L

Was this answer helpful?

Answer:

1) 540 km

2) 6 liters of petrol

Step-by-step explanation:

To answer the two questions, it is easiest to fist find the relationship between kilometers (km) and liters of petrol. Since 7 liters (L) results in 315 km, we can find the km/liter petrol conversion factor (converts liters of petrol to km):

(315 km)/(7 liters) = 45 km/L

1) 12 liters times the conversion factor will tell us how many km the motorcycle will travel"

(12 liters)*(45 km/liter) = 540 km [Note that the liters unit cancles, leaving only km]

2) To find the liters of petrol to travel 270 km, we can use the same conversion factor, but now we need to divide to get the units we want, which is km:

(270 km)/(45 km/l) = 6 liters [Note that km cancels and l moves to the top, leaving liters as the only unit.

He spent $200 on 0 tickets for children, 10 tickets for adults, and 20 tickets for seniors.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Total number of tickets brought=30

Total amount paid=$200

Cost of kid ticket=$3.5

Cost of adult ticket=$8

Cost of senior ticket=$6

Let x, y, z be the number of tickets brought for kid, adult, senior.

x+y+z=30

3.5x+8y+6z=200

2y=x+z

x+y+z=30

3y=30

y=10

x+z=20

z=20-x

3.5x+80+6(20-x)=200

3.5x+80+120-6x=200

2.5x=0

x=0

z=20

He bought 0 tickets for kid, 10 tickets for adult and 20 tickets for senior with an amount of $200.

To know more about equation,

https://brainly.com/question/649785

#SPJ4

[tex]A = 20,000 (1-0.12)^x[/tex] this equation shows the value of Marisa's car over a period of x years. Using the concept of depreciation we get this -

Depreciation is an accounting technique for spreading out the expense of a tangible item over the course of its useful life. Depreciation is a measure of how much an asset has been utilized for. It enables businesses to purchase assets over a predetermined length of time and generate income from those assets.

Given that,

Marisa buys a car for $20,000 = P

depreciates at a rate of 12% per year = r

and t is the for the time period.

As we know,

[tex]A = P (1-r)^t[/tex]

Where, A is the value of object after x period of time.

The value of Terrence's car after x years is:

[tex]A = 20,000 (1-0.12)^x[/tex]

Hence, the value of Marisa's car after x years is: [tex]A = 20,000 (1-0.12)^x[/tex]

To know more about depreciation refer to:

https://brainly.com/question/1203926

#SPJ1

Answer:f(x)=20,000(.12)^x

Step-by-step explanation:

took test

Because when two linear equations graph this very same line, a system of two linear simultaneous equations variables cannot be solved.

A linear equation seems to be an algebraic equation of something like the form y=mx+b, where m is the slope as well as b is the y-intercept, and only a constant and an initial-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

2x+6y=-28       (i)

x + 3y = -14      (ii)

Subtract 3y from both sides of the equation(ii)

[tex]\begin{matrix}&x=-14-3y\\&2x+6y=-28\\\end{matrix}[/tex]

Replace all occurrences of x with -14-3y in each equation.

Replace all occurrences of x in 2x+6y=-28 with -14-3y.

[tex]\begin{matrix}&2(-14-3y)+6y=-28\\&x=-14-3y\\\end{matrix}[/tex]

Simplify the left side.

Simplify 2(-14-3y)+6y.

[tex]\begin{matrix}&\ -28=-28\\&x=-14-3y\\\end{matrix}[/tex]

Remove any equations from the system that are always true.

[tex]x=-14-3 y[/tex]

there is no solution for the given equation.

To know more about linear equations visit:

https://brainly.com/question/29739212

#SPJ1

Answer:

Step-by-step explanation:

answer is b

Answer: c=9                                                            

Step-by-step explanation:

If LMNO is a parallelogram then NM=7=OL and the value of X is 7 unit

What is a Parallelogram?

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.

As it is a parallelogram so, the opposite sides of the parallelogram are equal so NM=OL and ON=LM ,

according to the question ;-

NM = x+5

OL=2x+3

and NM=OL

x+5=2x+3

x=2

So, NM= 7

OL=7

Learn more about Parallelogram from the link below

https://brainly.com/question/11220936

#SPJ1

Answer:

ED

Step-by-step explanation:

They both have side ED in their triangles!

Answer:

163 rounded to the nearest ten = 160.

Step-by-step explanation:

yes since 163 is not 165 or greater its 160 but if it the number was greater than 165 than it would be 170. in this case its not so the answer would be 160.

Answer: If 4/9 of the fish have a red stripe, we can determine the total number of fish in the tank by dividing the number of fish with red stripes by the fraction of fish with red stripes. This gives us 12 / (4/9) = 12 * (9/4) = 27 fish. So, there are 27 fish in the tank.

[tex] \frac{4}{9} x = 12[/tex]

[tex]x = 12 \times \frac{9}{4} [/tex]

[tex]12 \times 9 = 108[/tex]

[tex]4 \times 1 = 4[/tex]

[tex]x = \frac{108}{4} [/tex]

[tex]x = 27[/tex]

There are 27 fish in the tank. Hope this helps.

By solving linear inequation, it can be calculated that

The system of linear inequation represented by the graph is

x - y ≥ -8

3x + y ≥ -8

What is linear inequation?

Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by >,<, ≥, ≤

A one degree inequation is known as linear inequation.

Here,

One line passes through (0, 8) and (-1, 7)

Slope of the line = [tex]\frac{7-8}{-1-0}[/tex] = 1

Equation of line

y - 8 = 1(x - 0)

y - 8 = x

x - y = -8

Other line passes through (-4, 4) and (-3, 1)

Slope of the line = [tex]\frac{1-4}{-3-(-4)}[/tex] = -3

Equation of line

y - 4 = -3(x - (-4))

y - 4  = -3x - 12

3x + y = 4 - 12

3x + y = -8

Now the lines are solid lines

So equality is maintained

(0, 0) is inside the shaded region

So the system of linear inequation represented by the graph is

x - y ≥ -8

3x + y ≥ -8

To learn more about linear inequation, refer to the link-

https://brainly.com/question/24372553

#SPJ1

For the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.

Box and whiskers plot is the way of representation of data which gives the graphical image of the data set to understand better. In this the data is represented with the help of quartile.

The minimum and the maximum values in the box plot is plotted at the end points.

The following set of data which i s given in the problem.

3, 4, 5, 6, 6, 7, 7, 12, 13, 14, 14, 15, 15, 16, 17

Min: 3

The minimum value in the given data is 3. Thus, the min is 3.

Q1:6

First quartile appears at 6. Thus, the value of Q1 is 6.

Med:12

The middle value of the given data is 12 which appears at the center of all the values. Thus the med is 12.

Q3:14.5

Second quartile appears at 14.5. Thus, the value of  second quartile Q2 is 6.

Max: 17

The minimum value in the given data is 17 as shown in the image attached below. Thus, the min is 17.

Hence, for the box and whiskers plot for the following set of data the value of Min is 3, Q1 is 6, Med is 12, Q3 is 14.5 and Max is 17.

The complete question is : Answer the statistical measures and create a box and whiskers plot for the following set of data. You may optionally click and drag the numbers into numerical order.

3, 4, 5, 6, 6, 7, 7, 12, 13, 14, 14, 15, 15, 16, 17

3,4,5,6,6,7,7,12,13,14,14,15,15,16,17

Min:

Q1:

Med:

Q3:

Max:

To learn more about box and whiskers plot refer to :

https://brainly.com/question/19969646

#SPJ1

now, we're assuming the rate of 3.5% is for a simple interest account, so

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$900\\ P=\textit{original amount deposited}\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\dotfill &2.5 \end{cases} \\\\\\ 900=P[1+(0.035)(2.5)] \implies 900=P(1.0875) \\\\\\ \cfrac{900}{1.0875}=P\implies 827.59\approx P[/tex]

The equation for the relationship between the regular price (r) and the neighbor's price (n) will be r - n = 250.

A mathematical expression with an equals sign is referred to as an equation.

Algebra is widely used in equations.

When performing calculations but unsure of the precise number, algebra is used.

Linear equations: Any equation that can be expressed as ax + by + c = 0, where a, b, and c are all real numbers and a and b are not equal to zero.

In light of the posed query.

Khalid keeps bees and sells honey from them.

Additionally, n stands for the neighbor's honey price in dollars and r stands for the ordinary honey price in dollars.

We can determine the discount from the provided information.

7 - 4.50 = 2.50

8 - 5.50 = 2.50

10 - 7.50 = 2.50

12 - 9.50 = 2.50

Khalid gives his neighbor $2.50.

The equation for the link between the regular price r and the neighbor's price n will therefore be: r - n = 250

Therefore, the equation for the relationship between the regular price (r) and the neighbor's price (n) will be r - n = 250.

Know more about equations here:

https://brainly.com/question/28937794

#SPJ4

Complete question:

Khalid raises bees and sells the honey. He gives a discount to his neighbors. The table shows the neighbors' price, n, of buying honey that has a regular price of r dollars. Write an equation that represents the relationship. I put two pictures below to help. :)

Answer: r - n = 2.5

Step-by-step explanation: Took Quiz

Answer:

l =  10 feet

m = 30 feet

n = 25 feet

Total Perimeter = 65 feet

Step-by-step explanation:

The perimeter of a trianlge is the sum of its three sides, and in this case is equal to 65 feet.

65 feet = l + m + n

l + m + n = 65

We also know that:

 l = (1/3)m, and

n = l+m-15

Substitute these definitions of l and n into the original equation:

l + m + n = 65

[(1/3)m] + m + [l+m-15] = 65

[(1/3)m] + m + [[(1/3)m]+m-15] = 65

Simplify:

(1/3)m + m + (1/3)m + m - 15 = 65

2m + (2/3)m = 80

(6/3)m + (2/3)m = 80

(8/3)m = 80

m = 80*(3/8)

m = (10)*(3)

m = 30 feet

Since l = (1/3)m, l = 10 feet

Since n = l+m-15, n = 10 + 30 - 15, or 25 feet

The three sides are

      l:    10 feet

     m:  30 feet

     n:   25 feet

Total = 65 feet

Answer:

m = 7

Step-by-step explanation:

6 + 6 + 7 = 19.

You're welcome.

Answer: x= 5  y= -2

Step-by-step explanation: Time 2 to eliminate the y

6x - 4y = 38

5x + 4y =17

11x = 55

x= 5

Then put 5 in for the x, and you will get,  y = -2

Solution for the equation x² + 81 = 0 is x =  ± 9i.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

x² + 81 = 0

To find the solution of the given equation,

Simplify the equation,

x² = -81

x = √-81

x = ±9√-1

Since, i = √-1

x = ± 9i

The solution for the given equation is x =  ± 9i.

To know more about Equation on:

brainly.com/question/187506

#SPJ1

Answer:

Note that with embedded parentheses (parentheses within parenthesis), you always perform operations inside out; do the math on the inside before the outside. Note that if you have an absolute value | | sign which means take the positive value only of a number inside.

Answer: Absolute Value is the first level.

Step-by-step explanation:

2 |-10|

2 * 10

20

Answer:

Step-by-step explanation:

3x+8 = x-6

x=?

3x + 8 = x - 6

2x = -14

x = -7

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

check

3 × (-7) + 8 = -7 - 6

-21 + 8 = -13

-13 = -13

the answer is good